Anomalous diffusion of random walk on random planar maps
From MaRDI portal
Publication:2200505
DOI10.1007/s00440-020-00986-7zbMath1471.60160arXiv1807.01512OpenAlexW3044551581MaRDI QIDQ2200505
Publication date: 22 September 2020
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1807.01512
Geometric probability and stochastic geometry (60D05) Stochastic (Schramm-)Loewner evolution (SLE) (60J67) Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.) (60K50)
Related Items
Random walks on mated-CRT planar maps and Liouville Brownian motion ⋮ Spectral dimension, Euclidean embeddings, and the metric growth exponent ⋮ Percolation on Triangulations: A Bijective Path to Liouville Quantum Gravity ⋮ Relations between scaling exponents in unimodular random graphs ⋮ Existence and uniqueness of the Liouville quantum gravity metric for \(\gamma \in (0, 2)\) ⋮ A distance exponent for Liouville quantum gravity ⋮ The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds ⋮ How fast planar maps get swallowed by a peeling process ⋮ Random walk on random planar maps: spectral dimension, resistance and displacement ⋮ External diffusion-limited aggregation on a spanning-tree-weighted random planar map ⋮ The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity ⋮ Harmonic functions on mated-CRT maps ⋮ Quasisymmetric uniformization and heat kernel estimates ⋮ Chemical subdiffusivity of critical 2D percolation ⋮ Conformal growth rates and spectral geometry on distributional limits of graphs ⋮ Collisions of random walks in dynamic random environments ⋮ Recurrence of the uniform infinite half-plane map via duality of resistances
Cites Work
- Imaginary geometry. I: Interacting SLEs
- Liouville Brownian motion
- Conformal weldings of random surfaces: SLE and the quantum gravity zipper
- Markov type and threshold embeddings
- Uniqueness and universality of the Brownian map
- The Brownian map is the scaling limit of uniform random plane quadrangulations
- On the Riemann surface type of random planar maps
- A contour line of the continuum Gaussian free field
- Random walks on disordered media and their scaling limits. École d'Été de Probabilités de Saint-Flour XL -- 2010
- Ergodic theory on stationary random graphs
- Gaussian multiplicative chaos and applications: a review
- The Brownian plane
- Diffusion in planar Liouville quantum gravity
- Quantum gravity and inventory accumulation
- Liouville quantum gravity and KPZ
- Boundaries of planar graphs, via circle packings
- Unimodular hyperbolic triangulations: circle packing and random walk
- A mating-of-trees approach for graph distances in random planar maps
- Bijective counting of tree-rooted maps and shuffles of parenthesis systems
- Random walk on the incipient infinite cluster for oriented percolation in high dimensions
- The Alexander-Orbach conjecture holds in high dimensions
- Subdiffusive behavior of random walk on a random cluster
- Markov chains, Riesz transforms and Lipschitz maps
- The Brunn-Minkowski inequality in Gauss space
- Uniform infinite planar triangulations
- Growth and percolation on the uniform infinite planar triangulation
- Liouville Brownian motion and thick points of the Gaussian free field
- The hyperbolic Brownian plane
- The scaling limit of random simple triangulations and random simple quadrangulations
- Imaginary geometry. IV: Interior rays, whole-plane reversibility, and space-filling trees
- Joint convergence of random quadrangulations and their cores
- A distance exponent for Liouville quantum gravity
- How fast planar maps get swallowed by a peeling process
- Recurrence of distributional limits of finite planar graphs
- Recurrence of planar graph limits
- The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds
- Natural parametrization of SLE: the Gaussian free field point of view
- An almost sure KPZ relation for SLE and Brownian motion
- Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field
- Harmonic functions on mated-CRT maps
- Discrete uniformizing metrics on distributional limits of sphere packings
- Heat kernel for Liouville Brownian motion and Liouville graph distance
- Indistinguishability of trees in uniform spanning forests
- Bijective counting of Kreweras walks and loopless triangulations
- Simple random walk on the uniform infinite planar quadrangulation: Subdiffusivity via pioneer points
- Basic properties of the infinite critical-FK random map
- Active spanning trees with bending energy on planar maps and SLE-decorated Liouville quantum gravity for \(\kappa>8\)
- Bipolar orientations on planar maps and \(\mathrm{SLE}_{12}\)
- Processes on unimodular random networks
- Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces
- An elementary approach to Gaussian multiplicative chaos
- Gaussian free fields for mathematicians
- Probability on Trees and Networks
- Applications of a Planar Separator Theorem
- An approximation of partial sums of independent RV's, and the sample DF. II
- Brownian Motion and Harmonic Analysis on Sierpinski Carpets
- Multidimensional version of the results of Komlos, Major and Tusnady for vectors with finite exponential moments
- Upper Bounds on Liouville First‐Passage Percolation and Watabiki's Prediction
- Quasisymmetric uniformization and heat kernel estimates
- Random Fields and Geometry
- On the Enumeration of Tree-Rooted Maps
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item