Asymptotic behaviors of random walks on countable groups
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 …
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
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 …
small total displacement in terms of the spectral and isoperimetric profiles of the group. This …
Poisson boundary of group extensions
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 …
triviality of the Poisson-Furstenberg boundary (which is equivalent to the existence of non …
No percolation at criticality on certain groups of intermediate growth
No Percolation at Criticality on Certain Groups of Intermediate Growth | International
Mathematics Research Notices | Oxford Academic Skip to Main Content Advertisement Oxford …
Mathematics Research Notices | Oxford Academic Skip to Main Content Advertisement Oxford …
On the boundary at infinity for branching random walk
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 …
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
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) …
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
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 …
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
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 …
random walks that are allowed to take long jumps along multiple subgroups according to …
Liouville property for groups and conformal dimension
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 …
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
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 …
random walks that are allowed to take long jumps along multiple subgroups according to …