Probability on Trees and Networks
From MaRDI portal
Publication:2833171
DOI10.1017/9781316672815zbMath1376.05002OpenAlexW121824094MaRDI QIDQ2833171
Publication date: 17 November 2016
Full work available at URL: https://doi.org/10.1017/9781316672815
branching processesrandom walkscapacitypercolationisoperimetric inequalitiesHausdorff dimensionmass-transport techniquerandom walks on Galton-Watson trees
Trees (05C05) Small world graphs, complex networks (graph-theoretic aspects) (05C82) Random graphs (graph-theoretic aspects) (05C80) Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Analytic circuit theory (94C05) Random walks on graphs (05C81)
Related Items
Mehler’s Formula, Branching Process, and Compositional Kernels of Deep Neural Networks, On the peel number and the leaf-height of Galton–Watson trees, The power of two choices for random walks, The diameter of the uniform spanning tree of dense graphs, Symmetric Measures, Continuous Networks, and Dynamics, Connectedness of spheres in Cayley graphs, Weighted Message Passing and Minimum Energy Flow for Heterogeneous Stochastic Block Models with Side Information, Sub-tree counts on hyperbolic random geometric graphs, Factor of IID Percolation on Trees, Harmonic analysis on graphs via Bratteli diagrams and path-space measures, Abelian networks IV. Dynamics of nonhalting networks, Cover time for branching random walks on regular trees, Routeing on trees, The Sandpile Cellular Automaton, The CRT is the scaling limit of random dissections, Density and trace results in generalized fractal networks, Optimal Control for Diffusions on Graphs, Random non-crossing plane configurations: A conditioned Galton-Watson tree approach, Approximation on slabs and uniqueness for inhomogeneous percolation with a plane of defects, Random fractals and their intersection with winning sets, An Electric Network for Nonreversible Markov Chains, Minimal Transport Networks with General Boundary Conditions, Persistent Laplacians: Properties, Algorithms and Implications, Connective constants and height functions for Cayley graphs, Leaf multiplicity in a Bienaym\'e-Galton-Watson tree, Monotonicity for continuous-time random walks, Riesz transform for a flow Laplacian on homogeneous trees, Subcritical connectivity and some exact tail exponents in high dimensional percolation, Self-destructive percolation as a limit of forest-fire models on regular rooted trees, Random walk hitting times and effective resistance in sparsely connected Erdős‐Rényi random graphs, Rates of convergence for Gibbs sampling in the analysis of almost exchangeable data, Factor-of-iid balanced orientation of non-amenable graphs, A factor of i.i.d. with uniform marginals and infinite clusters spanned by equal labels, On the probabilistic representation of the free effective resistance of infinite graphs, Site percolation and isoperimetric inequalities for plane graphs, Limit Set of Branching Random Walks on Hyperbolic Groups, Slightly supercritical percolation on non‐amenable graphs I: The distribution of finite clusters, Broadcasting‐induced colorings of preferential attachment trees, Tuza's conjecture for random graphs, Ising percolation in the hyperbolic plane, Continuity of the Ising phase transition on nonamenable groups, New Hilbert space tools for analysis of graph Laplacians and Markov processes, Multiple random walks on graphs: mixing few to cover many, Random walk speed is a proper function on Teichmüller space, Quantitative Russo-Seymour-Welsh for random walk on random graphs and decorrelation of uniform spanning trees, Cosh gradient systems and tilting, Parking on the integers, A variational formula for large deviations in first-passage percolation under tail estimates, Mixing time and cutoff for one-dimensional particle systems, An invariance principle and a large deviation principle for the biased random walk on, Unnamed Item, Macroscopic loops in the \(3 d\) double-dimer model, Unnamed Item, Determinant-Preserving Sparsification of SDDM Matrices, Unnamed Item, A Class of Random Cantor Measures, with Applications, A random Schrödinger operator associated with the Vertex Reinforced Jump Process on infinite graphs, Hausdorff spectrum of harmonic measure, Nonuniqueness and mean-field criticality for percolation on nonunimodular transitive graphs, A Tits alternative for topological full groups, Extrema of the Two-Dimensional Discrete Gaussian Free Field, Self-Avoiding Walks and Connective Constants, Approximation of the Diagonal of a Laplacian’s Pseudoinverse for Complex Network Analysis, Extensive amenability and an application to interval exchanges, Non-Gaussian fluctuations of randomly trapped random walks, Lyons‐Pemantle‐Peres Monotonicity Problem for High Biases, Proof of Aldous’ spectral gap conjecture, Routing complexity of faulty networks, Forests on wired regular trees, Separately superharmonic functions in product networks, A note on Liouville type equations on graphs, UNIFORM SPANNING FORESTS OF PLANAR GRAPHS, Differentiability of the speed of biased random walks on Galton-Watson trees, Principal eigenvalue for the random walk among random traps on \({\mathbb{Z}}^{d}\), Strong noise sensitivity and random graphs, Cycle density in infinite Ramanujan graphs, Transience of the vacant set for near-critical random interlacements in high dimensions, Rotor Walks on Transient Graphs and the Wired Spanning Forest, Infinite and Giant Components in the Layers Percolation Model, Negative dependence and the geometry of polynomials, Speeding up non-Markovian first-passage percolation with a few extra edges, Random systems in ultrametric spaces, Infinite-step stationarity of rotor walk and the wired spanning forest, Trajectories in random minimal transposition factorizations, Counterexamples for percolation on unimodular random graphs, Invariant 𝜌-percolation on regular trees, New Bounds for Edge-Cover by Random Walk, Biased random walks on random graphs, Topics in Markov chains: mixing and escape rate, COVER TIME FOR THE FROG MODEL ON TREES, Geometry of Uniform Spanning Forest Components in High Dimensions, Negative association in uniform forests and connected graphs, Furstenberg entropy of intersectional invariant random subgroups, Almost Giant Clusters for Percolation on Large Trees with Logarithmic Heights, Abelian oil and water dynamics does not have an absorbing-state phase transition, Brownian motion on graph-like spaces, Some criteria for circle packing types and combinatorial Gauss-Bonnet Theorem, Action convergence of operators and graphs, Resistance forms, quasisymmetric maps and heat kernel estimates, Invariance under quasi-isometries of subcritical and supercritical behavior in the Boolean model of percolation, Energy randomness, Constrained percolation in two dimensions, The scaling limits of the minimal spanning tree and invasion percolation in the plane, The velocity of 1d Mott variable-range hopping with external field, Biased random walks on the interlacement set, Effective resistances and Kirchhoff index of ladder graphs, Noise-stability and central limit theorems for effective resistance of random electric networks, Harmonic analysis invariants for infinite graphs via operators and algorithms, Branching frequency and Markov entropy of repetition-free languages, Limits of the boundary of random planar maps, Random infinite squarings of rectangles, Kakeya-type sets over Cantor sets of directions in \(\mathbb {R}^{d+1}\), Percolation and isoperimetry on roughly transitive graphs, The local limit of the uniform spanning tree on dense graphs, Random walk on the range of random walk, Level-set percolation for the Gaussian free field on a transient tree, Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters, Estimation of flows in flow networks, Cutoff on all Ramanujan graphs, Solvable and algebraic systems on infinite ladder, The random pseudo-metric on a graph defined via the zero-set of the Gaussian free field on its metric graph, Anchored expansion, speed and the Poisson-Voronoi tessellation in symmetric spaces, Indistinguishability of the components of random spanning forests, The discrete Laplacian of a 2-simplicial complex, Symmetric pairs of unbounded operators in Hilbert space, and their applications in mathematical physics, Invariant measures, Hausdorff dimension and dimension drop of some harmonic measures on Galton-Watson trees, Resistance growth of branching random networks, Uniform infinite half-planar quadrangulations with skewness, Approximate calculation of the defect of a Lipschitz cylindrical condenser, Invariant monotone coupling need not exist, Stable limit laws for randomly biased walks on supercritical trees, Cops and invisible robbers: the cost of drunkenness, The Gauss-Bonnet operator of an infinite graph, Disorder, entropy and harmonic functions, Self-avoiding walks and amenability, Electrical resistance of the low dimensional critical branching random walk, Extinction window of mean field branching annihilating random walk, Fractal percolation, porosity, and dimension, Finite size percolation in regular trees, Random walks on Galton-Watson trees with random conductances, The unscaled paths of branching Brownian motion, Spectral measures of factor of i.i.d. processes on vertex-transitive graphs, Mixing time of near-critical random graphs, Random walks on directed covers of graphs, Cover times, blanket times, and majorizing measures, Uniform infinite planar triangulations, Branching number of a pseudogroup, Non-robust phase transitions in the generalized clock model on trees, Exponential growth of ponds in invasion percolation on regular trees, Combinatorial bandits, Expected distance based on random walks, Random walks in random Dirichlet environment are transient in dimension \(d \geq 3\), On rigidity and convergence of circle patterns, Minimal configurations and sandpile measures, Microvascular networks with uniform flow, Percolation on a product of two trees, Heavy subtrees of Galton-Watson trees with an application to Apollonian networks, Cutting down trees with a Markov chainsaw, Random walk on the incipient infinite cluster for oriented percolation in high dimensions, Potential distribution on random electrical networks, Cut-off for lamplighter chains on tori: dimension interpolation and phase transition, Myopic models of population dynamics on infinite networks, Central limit theorems for biased randomly trapped random walks on \(\mathbb{Z}\), Harmonic Dirichlet functions on planar graphs, Sharp threshold for percolation on expanders, Biased random walks on Galton-Watson trees with leaves, Strongly correlated random interacting processes. Abstracts from the workshop held January 28 -- February 3, 2018, Dual graphs and modified Barlow-Bass resistance estimates for repeated barycentric subdivisions, On the spectrum of lamplighter groups and percolation clusters, Expansion of random graphs: new proofs, new results, Effective resistances for supercritical percolation clusters in boxes, Symmetric pairs and self-adjoint extensions of operators, with applications to energy networks, Aging of the Metropolis dynamics on the random energy model, A monotone isomorphism theorem, Minimal subfamilies and the probabilistic interpretation for modulus on graphs, On the spectral dimension of causal triangulations, A characterization of the locally finite networks admitting non-constant harmonic functions of finite energy, Analysis of the physical Laplacian and the heat flow on a locally finite graph, The TASEP speed process, Is the critical percolation probability local?, Scaling limit of the random walk among random traps on \(\mathbb Z^{d}\), Boundaries of planar graphs, via circle packings, Unimodular hyperbolic triangulations: circle packing and random walk, The disk-percolation model on graphs, Convergence, unanimity and disagreement in majority dynamics on unimodular graphs and random graphs, Percolation and local isoperimetric inequalities, The Williams-Bjerknes model on regular trees, Ultrametric and tree potential, \(k\)-independent percolation on trees, Coalescent random forests, Resistance bounds for first-passage percolation and maximum flow, Occupation measure of random walks and wired spanning forests in balls of Cayley graphs, The speed of the tagged particle in the exclusion process on Galton-Watson trees, Analyticity for rapidly determined properties of Poisson Galton-Watson trees, The cone percolation model on Galton-Watson and on spherically symmetric trees, Range and speed of rotor walks on trees, Kazhdan groups have cost 1, New dynamical invariants on hyperbolic manifolds, The boundary of a square tiling of a graph coincides with the Poisson boundary, Correlation bounds for fields and matroids, The number of spanning clusters of the uniform spanning tree in three dimensions, Homotopy types of random cubical complexes, The local limit of uniform spanning trees, Spatial networks and percolation. Abstracts from the workshop held January 17--23, 2021 (hybrid meeting), Local geometry of the rough-smooth interface in the two-periodic Aztec diamond, The wired arboreal gas on regular trees, Topology and geometry of random 2-dimensional hypertrees, Pedigree in the biparental Moran model, Recurrence of a weighted random walk on a circle packing with parabolic carrier, Recurrence versus transience for weight-dependent random connection models, Generalization of effective conductance centrality for egonetworks, Some inequalities for reversible Markov chains and branching random walks via spectral optimization, Logarithmic correction to resistance, Recurrence of planar graph limits, Random Dirichlet environment viewed from the particle in dimension \(d\geq 3\), Dirichlet forms and associated heat kernels on the Cantor set induced by random walks on trees, An interlacing technique for spectra of random walks and its application to finite percolation clusters, Monopoles, dipoles, and harmonic functions on Bratteli diagrams, Enumerative combinatorics of simplicial and cell complexes: Kirchhoff and Trent type theorems, Canonical measures on metric graphs and a Kazhdan's theorem, The parabolic Anderson model on a Galton-Watson tree, Finite-energy infinite clusters without anchored expansion, Local convergence of large critical multi-type Galton-Watson trees and applications to random maps, Transience and recurrence of random walks on percolation clusters in an ultrametric space, Scaling limits for sub-ballistic biased random walks in random conductances, Interlacements and the wired uniform spanning forest, The incipient infinite cluster of the uniform infinite half-planar triangulation, Metastability of hard-core dynamics on bipartite graphs, Spectral theory of infinite quantum graphs, A combinatorial proof of a formula of Biane and Chapuy, Size bias for one and all, Central limit theorem for exponentially quasi-local statistics of spin models on Cayley graphs, Random forests and networks analysis, Percolation on hyperbolic graphs, Long term behaviour of a reversible system of interacting random walks, Counting trees with random walks, The Dirichlet problem for orthodiagonal maps, Coloring percolation clusters at random., Scaling exponents of random walks in random sceneries., Enlargement of subgraphs of infinite graphs by Bernoulli percolation, Phase transitions in ferromagnetic Ising models with spatially dependent magnetic fields, The \(L^2\) boundedness condition in nonamenable percolation, The free energy in the Derrida-Retaux recursive model, Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution, On the tail of the branching random walk local time, Inverted orbits of exclusion processes, diffuse-extensive-amenability, and (non-?)amenability of the interval exchanges, Random walk on random planar maps: spectral dimension, resistance and displacement, Variable length memory chains: characterization of stationary probability measures, Continuum versus discrete networks, graph Laplacians, and reproducing kernel Hilbert spaces, On planar graphs of uniform polynomial growth, A reverse Aldous-Broder algorithm, Locality of connective constants, Stationary determinantal processes on \({\mathbb{Z}}^d\) with \(N\) labeled objects per site. I: Basic properties and full domination, Second-order term of cover time for planar simple random walk, Directed polymers on infinite graphs, Typical behavior of the harmonic measure in critical Galton-Watson trees with infinite variance offspring distribution, Conservative and semiconservative random walks: recurrence and transience, On transience of frogs on Galton-Watson trees, Invariant embeddings of unimodular random planar graphs, The speed of random walk on Galton-Watson trees with vanishing conductances, Random walks with local memory, Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree, Power-law bounds for critical long-range percolation below the upper-critical dimension, Haldane's formula in Cannings models: the case of moderately strong selection, Route lengths in invariant spatial tree networks, Sufficient condition for root reconstruction by parsimony on binary trees with general weights, Polynomial localization of the 2D-vertex reinforced jump process, On the computational tractability of statistical estimation on amenable graphs, Conformal growth rates and spectral geometry on distributional limits of graphs, Scaling limits of the three-dimensional uniform spanning tree and associated random walk, Random walks on the discrete affine group, Large deviations for random walks on free products of finitely generated groups, The TASEP on Galton-Watson trees, Weights of uniform spanning forests on nonunimodular transitive graphs, Unimodular Hausdorff and Minkowski dimensions, Collisions of random walks in dynamic random environments, Scaling limits of tree-valued branching random walks, The TAZRP speed process, Uniform spanning forests on biased Euclidean lattices, Multicolour Poisson matching, Coexistence of competing first passage percolation on hyperbolic graphs, Once reinforced random walk on \(\mathbb{Z}\times\gamma\), On coprime percolation, the visibility graphon, and the local limit of the GCD profile, Metric graphs, cross ratios, and Rayleigh's laws, Coalescing and branching simple symmetric exclusion process, Return probabilities on nonunimodular transitive graphs, Mean field behavior during the big bang regime for coalescing random walks, The free uniform spanning forest is disconnected in some virtually free groups, depending on the generator set, On the Hilbert evolution algebras of a graph, Finding geodesics on graphs using reinforcement learning, Electrical flows over spanning trees, A mechanized proof of the max-flow min-cut theorem for countable networks with applications to probability theory, Unimodular measures on the space of all Riemannian manifolds, Absence of backward infinite paths for first-passage percolation in arbitrary dimension, Reversible Markov decision processes and the Gaussian free field, Explicit universal minimal constants for polynomial growth of groups, Sharp bounds on eigenvalues via spectral embedding based on signless Laplacians, Connectedness of the free uniform spanning forest as a function of edge weights, The trace-reinforced ants process does not find shortest paths, Indistinguishability of trees in uniform spanning forests, A zero-one law for recurrence and transience of frog processes, Diffusive estimates for random walks on stationary random graphs of polynomial growth, Harmonic pinnacles in the discrete Gaussian model, Asymptotic properties of expansive Galton-Watson trees, Shalom's property \(H_{\mathrm{FD}}\) and extensions by \(\mathbb{Z}\) of locally finite groups, Stochastic explosion and non-uniqueness for \(\alpha\)-Riccati equation, Growth of Lévy trees, On the derivation of mean-field percolation critical exponents from the triangle condition, The parabolic Anderson model on a Galton-Watson tree revisited, Invariant measures for iterated function systems with inverses, Random walk on the random connection model, Symmetric seminorms and the Leibniz property, Existence of phase transition for percolation using the Gaussian free field, Parameterised branching processes: a functional version of Kesten \& Stigum theorem, Random spanning forests and hyperbolic symmetry, The diameter of uniform spanning trees in high dimensions, Biased random walk on the trace of biased random walk on the trace of \(\dots\), A stationary planar random graph with singular stationary dual: dyadic lattice graphs, Phase transitions for a class of gradient fields, On the speed and spectrum of mean-field random walks among random conductances, Continuous versus discrete spins in the hyperbolic plane, Surviving ends in Bernoulli percolation on graphs roughly isometric to a tree, The existence phase transition for scale invariant Poisson random fractal models, Recurrence of Markov chain traces, Inhomogeneous percolation on ladder graphs, Recurrence and density decay for diffusion-limited annihilating systems, Escape regimes of biased random walks on Galton-Watson trees, Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for \(\kappa>8\), Random walk on barely supercritical branching random walk, Mean-field avalanche size exponent for sandpiles on Galton-Watson trees, A rotor configuration with maximum escape rate, Geometric bounds for convergence rates of averaging algorithms, Scaling limit of sub-ballistic 1D random walk among biased conductances: \textit{a story of wells and walls}, The frog model on non-amenable trees, Scaling limit for the ant in a simple high-dimensional labyrinth, Random walks on mated-CRT planar maps and Liouville Brownian motion, Universality and sharpness in activated random walks, Controllability, matching ratio and graph convergence, Sparse expanders have negative curvature, Transience and anchored isoperimetric dimension of supercritical percolation clusters, Locality of percolation for graphs with polynomial growth, Weighted self-avoiding walks, Every countable infinite group admits a long range percolation with a phase transition, Distribution of levels in high-dimensional random landscapes, Point processes, cost, and the growth of rank in locally compact groups, Transitions for exceptional times in dynamical first-passage percolation, Palm pairs and the general mass-transport principle, Non-intersection of transient branching random walks, Anomalous diffusion of random walk on random planar maps, A stochastic Ramsey theorem, Activated Random Walks on \(\mathbb{Z}^d\), Analysis on trees with nondoubling flow measures, Geometric amenability in totally disconnected locally compact groups, A spectral characterization for concentration of the cover time, Invariant spanning double rays in amenable groups, Extendable self-avoiding walks, Geometric and spectral properties of causal maps, Subdiffusivity of random walk on the 2D invasion percolation cluster, The Seneta-Heyde scaling for the branching random walk, Unions of random trees and applications, Asymptotic height distribution in high-dimensional sandpiles, On hitting times for a simple random walk on dense Erdös-Rényi random graphs, Speed of random walks, isoperimetry and compression of finitely generated groups, Hyper-positive definite functions I: scalar case, branching-type stationary stochastic processes, Almost sure behavior of linearly edge-reinforced random walks on the half-line, Time scale separation and dynamic heterogeneity in the low temperature East model, Infinite volume limit of the abelian sandpile model in dimensions \(d \geq 3\), Elementary fixed points of the BRW smoothing transforms with infinite number of summands, Decomposition and convergence for tree martingales, Sub-trees of a random tree, Supercritical causal maps: geodesics and simple random walk, Graph topologies induced by edge lengths, The branching-ruin number as critical parameter of random processes on trees, A deterministic walk on the randomly oriented Manhattan lattice, Potential theory on trees, graphs and Ahlfors-regular metric spaces, Polynomials Associated with Finite Markov Chains, Galton-Watson trees with vanishing martingale limit, Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field, Jump processes on the boundaries of random trees, Intrinsic Metrics on Graphs: A Survey, Universality of high-dimensional spanning forests and sandpiles, Recent results of quantum ergodicity on graphs and further investigation, The Algebraic Method in Tree Percolation, Boolean percolation on doubling graphs, A new discrete Hopf-Rinow theorem, Phase transitions for edge-reinforced random walks on the half-line, Harmonic functions on mated-CRT maps, Uniqueness and non-uniqueness for spin-glass ground states on trees, Condensation of a self-attracting random walk, The speed of biased random walk among random conductances, Statistical physics on a product of trees, Hyperbolic and parabolic unimodular random maps, Harmonic measure for biased random walk in a supercritical Galton-Watson tree, Linking and cutting spanning trees, A characterization of effective resistance metrics, Graphs of finite measure, Random walk on random infinite looptrees, Transience of edge-reinforced random walk, Resistance distances in Cayley graphs on symmetric groups, Relations between scaling exponents in unimodular random graphs, Most transient random walks have infinitely many cut times, Global information from local observations of the noisy voter model on a graph, Harnack inequality and one-endedness of UST on reversible random graphs, Geometry of random Cayley graphs of abelian groups, Scaling limits of loop-erased Markov chains on resistance spaces via a partial loop-erasing procedure, Gap at 1 for the percolation threshold of Cayley graphs, Doubly stochastic Yule cascades. II: The explosion problem in the non-reversible case, Random nearest neighbor graphs: the translation invariant case, Thin-ended clusters in percolation in, Triangulations of uniform subquadratic growth are quasi-trees, Crossings states and sets of states in random walks, A note on some critical thresholds of Bernoulli percolation, Random interlacement is a factor of i.i.d., Logarithmic corrections to scaling in the four-dimensional uniform spanning tree, Tropical moments of tropical Jacobians, Analyticity Results in Bernoulli Percolation, On the boundary at infinity for branching random walk, A subperiodic tree whose intermediate branching number is strictly less than the lower intermediate growth rate, Transience of simple random walks with linear entropy growth, Particle density in diffusion-limited annihilating systems, Models of random subtrees of a graph, Capacity of the range of random walks on groups, Asymptotic behaviors of random walks on countable groups, Spin systems with hyperbolic symmetry: a survey, Graph curvature via resistance distance, Unnamed Item
