2 citations · 3 across the 4 of their papers we have counts for
7 papers
Phase transition of disordered random networks on quasi-transitive graphs
Yuelin Liu, Kainan Xiang
Given a quasi-transitive infinite graph with volume growth rate a transient biased electric network with bias and a recur…
Limit set of branching random walks on hyperbolic groups
Vladas Sidoravicius, Longmin Wang, Kainan Xiang
Let be a nonelementary hyperbolic group with a word metric and its hyperbolic boundary equipped with a visual metric for some parameter . Fix a super…
The invariance principle and the large deviation for the biased random walk on
Yuelin Liu, Vladas Sidoravicius, Longmin Wang +1
In this paper, we establish the invariance principle and the large deviation for the biased random walk with on .
Uniform spanning forests associated with biased random walks on Euclidean lattices
Zhan Shi, Vladas Sidoravicius, He Song +2
The uniform spanning forest measure () on a locally finite, infinite connected graph with conductance is defined as a weak limit of uniform spanning tree meas…
On Spectral Radius of Biased Random Walks on Infinite Graphs
Zhan Shi, Vladas Sidoravicius, He Song +2
We consider a class of biased random walks on infinite graphs and present several general results on the spectral radius of biased random walk.
Cutpoints for Random Walks on Quasi-Transitive Graphs
He Song, Kainan Xiang
We prove that a simple random walk on quasi-transitive graphs with the volume growth being faster than any polynomial of degree 4 has a.s. infinitely many cut times, and hence infi…