4 citations · 13 across the 10 of their papers we have counts for
10 papers
Large deviation principle for empirical measures of once-reinforced random walks on finite graphs
Xiangyu Huang, Yong Liu, Kainan Xiang
A once-reinforced random walk (-ORRW) on connected graph is a self-interacting random walk which moves to its neighbors at each step according to the weights of the edges at…
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…
Locality of percolation critical probabilities: uniformly nonamenable case
He Song, Kai-Nan Xiang, Song-Chao-Hao Zhu
Let be a sequence of transitive infinite connected graphs with where each is bond percolation critical pro…
Connective Constants on Cayley Graphs
He Song, Kai-Nan Xiang, Song-Chao-Hao Zhu
For a transitive infinite connected graph , let be its connective constant. Denote by the set of Cayley graphs for finitely generated infinite groups wi…
Concentration properties of semi-vertex transitive graphs and random bi-coset graphs
Xingchao Deng, Kainan Xiang
It is well-known that concentrators are sparse graphs of high connectivity, which play a key role in the construction of switching networks; and any semi-vertex transitive graph is…