Disorder, entropy and harmonic functions

DOI10.1214/14-AOP934zbMath1337.60248arXiv1111.4853MaRDI QIDQ888529

Ariel Yadin, Hugo Duminil-Copin, Gady Kozma, Itai Benjamini

Publication date: 30 October 2015

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.4853

zbMATH Keywords

entropypercolationheat kernelharmonic functionsrandom walkanomalous diffusionrandom environmentscorrectoranchored Poincaré inequalityanchored volume doubling propertygraphic fractalsmacroscopic ballsstationary environment

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Diffusion processes (60J60) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Percolation (82B43) Processes in random environments (60K37) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Probabilistic methods in group theory (20P05)

Related Items (28)

Diffusive estimates for random walks on stationary random graphs of polynomial growth ⋮ An elliptic Harnack inequality for difference equations with random balanced coefficients ⋮ A Liouville theorem for elliptic systems with degenerate ergodic coefficients ⋮ Local limit theorems for the random conductance model and applications to the Ginzburg-Landau \(\nabla \phi\) interface model ⋮ Supercritical loop percolation on \(\mathbb{Z}^d\) for \(d \geq 3\) ⋮ Annealed estimates on the Green function ⋮ Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held October 30 -- November 5, 2022 ⋮ Stochastic Homogenization of Linear Elliptic Equations: Higher-Order Error Estimates in Weak Norms Via Second-Order Correctors ⋮ Liouville Principles and a Large-Scale Regularity Theory for Random Elliptic Operators on the Half-Space ⋮ Sparse expanders have negative curvature ⋮ Transience and anchored isoperimetric dimension of supercritical percolation clusters ⋮ Harnack inequality and one-endedness of UST on reversible random graphs ⋮ Recent progress on the random conductance model ⋮ Effective multipoles in random media ⋮ Harmonic functions of linear growth on solvable groups ⋮ Optimal corrector estimates on percolation cluster ⋮ Sublinear growth of the corrector in stochastic homogenization: optimal stochastic estimates for slowly decaying correlations ⋮ A functional analysis proof of Gromov's polynomial growth theorem ⋮ Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters ⋮ SPDE limit of weakly inhomogeneous ASEP ⋮ A higher-order large-scale regularity theory for random elliptic operators ⋮ Chemical subdiffusivity of critical 2D percolation ⋮ Comparing mixing times on sparse random graphs ⋮ A regularity theory for random elliptic operators ⋮ Pointer chasing via triangular discrimination ⋮ An efficient algorithm for solving elliptic problems on percolation clusters ⋮ Polynomials and harmonic functions on discrete groups ⋮ Polynomial growth harmonic functions on groups of polynomial volume growth

Cites Work

• Invariance principle for Mott variable range hopping and other walks on point processes
• Harmonic maps on amenable groups and a diffusive lower bound for random walks
• Ergodic theory on stationary random graphs
• Harmonic deformation of Delaunay triangulations
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• Quasi-diffusion in a 3D supersymmetric hyperbolic sigma model
• Homomorphisms to \(\mathbb R\) constructed from random walks
• Scaling for a one-dimensional directed polymer with boundary conditions
• Quenched invariance principle for random walks in balanced random environment
• Gaussian estimates for Markov chains and random walks on groups
• Anomalous heat-kernel decay for random walk among bounded random conductances
• The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
• An invariance principle for reversible Markov processes. Applications to random motions in random environments
• Quenched invariance principle for simple random walk on percolation clusters
• The Alexander-Orbach conjecture holds in high dimensions
• Parabolic Harnack inequality and local limit theorem for percolation clusters
• The incipient infinite cluster in two-dimensional percolation
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains
• Subdiffusive behavior of random walk on a random cluster
• Random walks on discrete groups: Boundary and entropy
• Symmetric Markov chains in \({\mathbb{Z}}^ 4:\) How fast can they move?
• Weak convergence of a random walk in a random environment
• Harmonic functions on manifolds
• Parabolic Harnack inequality and estimates of Markov chains on graphs
• Green's functions for elliptic and parabolic equations with random coefficients
• Random walks on supercritical percolation clusters
• The incipient infinite cluster for high-dimensional unoriented percolation
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Recurrence of distributional limits of finite planar graphs
• Incipient infinite percolation clusters in 2D.
• Cut points and diffusive random walks in random environment
• Which values of the volume growth and escape time exponent are possible for a graph?
• Quenched invariance principles for walks on clusters of percolation or among random conduc\-tances
• Invariance principle for the random conductance model with unbounded conductances
• Simple random walk on the uniform infinite planar quadrangulation: Subdiffusivity via pioneer points
• A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment
• Functional CLT for random walk among bounded random conductances
• Processes on unimodular random networks
• Local limit of labeled trees and expected volume growth in a random quadrangulation
• High-dimensional incipient infinite clusters revisited
• A Poisson formula for semi-simple Lie groups
• On the chemical distance for supercritical Bernoulli percolation
• On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to \(\nabla\varphi\) interface model
• Probability on Trees and Networks
• Continuity of Solutions of Parabolic and Elliptic Equations
• A new proof of Gromov’s theorem on groups of polynomial growth
• On Harnack's theorem for elliptic differential equations
• A note on the isoperimetric constant
• Harmonic functions on complete riemannian manifolds
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Random Walks on Infinite Graphs and Groups - a Survey on Selected topics
• Real Analysis and Probability
• Ergodic theory on Galton—Watson trees: speed of random walk and dimension of harmonic measure
• Quenched invariance principles for random walks on percolation clusters
• Stochastic homogenization of horospheric tree products
• Harmonic functions on planar and almost planar graphs and manifolds, via circle packings
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Disorder, entropy and harmonic functions