Asymptotic behaviors of random walks on countable groups

T Zheng - Proceedings of the International Congress of …, 2022‏ - content.ems.press
Asymptotic behaviors of random walks on countable groups Page 1 Asymptotic behaviors of
random walks on countable groups Tianyi Zheng (郑天一) Abstract In this note we survey some …

Small-ball estimates for random walks on groups

T Hutchcroft - arxiv preprint arxiv:2406.17587, 2024‏ - arxiv.org
We prove a new inequality bounding the probability that the random walk on a group has
small total displacement in terms of the spectral and isoperimetric profiles of the group. This …

Poisson boundary of group extensions

A Erschler, J Frisch - arxiv preprint arxiv:2206.11111, 2022‏ - arxiv.org
Given a finitely generated group, the well-known Stability Problem asks whether the non-
triviality of the Poisson-Furstenberg boundary (which is equivalent to the existence of non …

No percolation at criticality on certain groups of intermediate growth

J Hermon, T Hutchcroft - International Mathematics Research …, 2021‏ - academic.oup.com
No Percolation at Criticality on Certain Groups of Intermediate Growth | International
Mathematics Research Notices | Oxford Academic Skip to Main Content Advertisement Oxford …

On the boundary at infinity for branching random walk

E Candellero, T Hutchcroft - Electronic Communications in …, 2023‏ - projecteuclid.org
We prove that a supercritical branching random walk on a transient Markov chain converges
almost surely under rescaling to a random measure on the Martin boundary of the …

A relation between isoperimetry and total variation decay with applications to graphs of non-negative Ollivier-Ricci curvature

T Hutchcroft, IM Lopez - arxiv preprint arxiv:2411.04988, 2024‏ - arxiv.org
We prove an inequality relating the isoperimetric profile of a graph to the decay of the
random walk total variation distance $\sup_ {x\sim y}|| P^ n (x,\cdot)-P^ n (y,\cdot) …

Collisions of random walks in dynamic random environments

N Halberstam, T Hutchcroft - Electronic Journal of Probability, 2022‏ - projecteuclid.org
We study dynamic random conductance models on Z 2 in which the environment evolves as
a reversible Markov process that is stationary under space-time shifts. We prove under a …

Long range random walks and associated geometries on groups of polynomial growth

ZQ Chen, T Kumagai, L Saloff-Coste, J Wang… - arxiv preprint arxiv …, 2018‏ - arxiv.org
In the context of countable groups of polynomial volume growth, we consider a large class of
random walks that are allowed to take long jumps along multiple subgroups according to …

Liouville property for groups and conformal dimension

NM Bon, V Nekrashevych, T Zheng - arxiv preprint arxiv:2305.14545, 2023‏ - arxiv.org
Conformal dimension is a fundamental invariant of metric spaces, particularly suited to the
study of self-similar spaces, such as spaces with an expanding self-covering (eg Julia sets of …

Long range random walks and associated geometries on groups of polynomial growth

ZQ Chen, T Kumagai, L Saloff-Coste, J Wang… - Annales de l'Institut …, 2022‏ - numdam.org
In the context of countable groups of polynomial volume growth, we consider a large class of
random walks that are allowed to take long jumps along multiple subgroups according to …