9 papers · 1 filter
Large deviations for maximum local time of simple random walk in dimensions
Xinyi Li, Yushu Zheng
We obtain sharp asymptotic probabilities for upward deviations of the maximum local time of discrete- and continuous-time simple random walks on , . For downw…
Tail exponents of the three-dimensional uniform spanning tree and Abelian sandpile
Xinyi Li, Runsheng Liu, Daisuke Shiraishi
We study the local geometry of the three-dimensional uniform spanning tree and its connection with the Abelian sandpile model. We obtain sharp tail exponents, up to subpolynomial e…
Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup
Yifan Gao, Ruixuan Li, Xinyi Li
We study generalized non-intersection probabilities for the three-dimensional Brownian loop soup at subcritical intensities. We establish the existence of generalized intersection…
Favorite sites for simple random walk in two and more dimensions
Chenxu Hao, Xinyi Li, Izumi Okada +1
On the trace of a discrete-time simple random walk on for , we consider the evolution of favorite sites, i.e., sites that achieve the maximal local time at…
Asymptotics for the percolation threshold of finitary random interlacements in four and higher dimensions
Yijie Bi, Zhenhao Cai, Xinyi Li +2
We establish sharp asymptotic bounds for the critical intensity of the Finitary Random Interlacements (FRI) model in four and higher dimensions with general trajectory length distr…
Full extremal process in four-dimensional membrane model
Hao Ge, Xinyi Li, Jiaxi Zhao
We investigate the extremal process of four-dimensional membrane models as the size of the lattice tends to infinity. We prove the cluster-like geometry of the extreme points a…