Asymptotic behaviors of random walks on countable groups

DOI10.4171/icm2022/138OpenAlexW4389774873MaRDI QIDQ6200306

Publication date: 22 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/icm2022/138

zbMATH Keywords

harmonic functions volume growth random walks on groups

Mathematics Subject Classification ID

Asymptotic properties of groups (20F69) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

Cites Work

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Local asymptotics for controlled martingales
Cantor systems, piecewise translations and simple amenable groups
Harmonic maps on amenable groups and a diffusive lower bound for random walks
Spectral distribution and $L^{2}$-isoperimetric profile of Laplace operators on groups
Groups of given intermediate word growth.
Harmonic functions of linear growth on solvable groups
Random walks and isoperimetric profiles under moment conditions
A Gaussian upper bound for martingale small-ball probabilities
$L_p$ compression, traveling salesmen, and stable walks.
On amenability of automata groups.
Poisson-Furstenberg boundary of random walks on wreath products and free metabelian groups.
Random walks driven by low moment measures
Occupation measure of random walks and wired spanning forests in balls of Cayley graphs
Gromov's theorem on groups of polynomial growth and elementary logic
Amenability via random walks.
Internal diffusion limited aggregation on discrete groups having exponential growth
Linear drift and Poisson boundary for random walks
Entropy and isoperimetry for linear and non-linear group actions.
Isoperimetric inequalities and Markov chains
On Burnside's problem on periodic groups
Instability of Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains
Random walks on discrete groups: Boundary and entropy
Elementary amenable groups
Ergodic and mixing random walks on locally compact groups
Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
Markov chains, Riesz transforms and Lipschitz maps
Isoperimetricity for groups and manifolds
A lower bound for the growth function of periods in Grigorchuk groups
Comparison techniques for random walk on finite groups
On-diagonal lower bounds for heat kernels and Markov chains
Harmonic forms with values in locally constant Hilbert bundles
Global existence theorems for harmonic maps to nonlocally compact spaces
On drift and entropy growth for random walks on groups
Random walks on weakly hyperbolic groups
Palindromic subshifts and simple periodic groups of intermediate growth
Harmonic analysis, cohomology, and the large-scale geometry of amenable groups
Ultracontractivity and Nash type inequalities
Strong approximate transitivity, polynomial growth, and spread out random walks on locally compact groups
Amenability of linear-activity automaton groups
Isoperimetric profile and random walks on locally compact solvable groups
The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
Finite-dimensional representations constructed from random walks
On the joint behaviour of speed and entropy of random walks on groups
Poisson boundaries of lamplighter groups: proof of the Kaimanovich-Vershik conjecture
Speed of random walks, isoperimetry and compression of finitely generated groups
Instability of the Liouville property for quasi-isometric graphs and manifolds of polynomial volume growth
Growth of periodic Grigorchuk groups
Choquet-Deny groups and the infinite conjugacy class property
Random walks on free solvable groups
The Choquet-Deny theorem and distal properties of totally disconnected locally compact groups of polynomial growth
Asymptotic entropy and Green speed for random walks on countable groups
Behaviors of entropy on finitely generated groups
Non-Liouville groups with return probability exponent at most 1/2
Extensions of amenable groups by recurrent groupoids
Growth of finitely generated solvable groups
A Poisson formula for semi-simple Lie groups
Growth of finitely generated solvable groups and curvature of Riemannian manifolds
Free subgroups in linear groups
Boundary behavior for groups of subexponential growth.
Probability on Trees and Networks
Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
Full Banach Mean Values on Countable groups.
Symmetric Random Walks on Groups
"MÜNCHHAUSEN TRICK" AND AMENABILITY OF SELF-SIMILAR GROUPS
Embeddings of Discrete Groups and the Speed of Random Walks
A new proof of Gromov’s theorem on groups of polynomial growth
The wreath product of $\mathbb {Z}$ with $\mathbb {Z}$ has Hilbert compression exponent $\frac {2}{3}$
DEGREES OF GROWTH OF FINITELY GENERATED GROUPS, AND THE THEORY OF INVARIANT MEANS
Amenability and paradoxical decompositions for pseudogroups and for discrete metric spaces
A functional analysis proof of Gromov's polynomial growth theorem
Speed Exponents of Random Walks on Groups
Extensive amenability and an application to interval exchanges
EXACTNESS AND UNIFORM EMBEDDABILITY OF DISCRETE GROUPS
Countable Amenable Identity Excluding Groups
Introduction to Analysis on Graphs
LOWER BOUNDS ON THE GROWTH OF A GROUP ACTING ON THE BINARY ROOTED TREE
ON A TORSION-FREE WEAKLY BRANCH GROUP DEFINED BY A THREE STATE AUTOMATON
Sobolev inequalities in disguise
Random Walks on Infinite Graphs and Groups
On the Gap Conjecture concerning group growth
Thompson's Group F is Not Liouville
Poisson boundaries and envelopes of discrete groups
Metric cotype
The Poisson formula for groups with hyperbolic properties
On the stability of the behavior of random walks on groups

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