Y. Abe

activity

20122025

most citedExceptional points of two-dimensional random walks at multiples of the cover time

12 citations · 37 across the 8 of their papers we have counts for

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8 papers · 1 filter

math.PR2025

Extremal process of the local time of simple random walk on a regular tree

Yoshihiro Abe, Marek Biskup

We study a continuous-time simple random walk on a regular rooted tree of depth $n$ in two settings: either the walk is started from a leaf vertex and run until the tree root is fi…

math.PR2019★ 6 cited

Exceptional points of discrete-time random walks in planar domains

Yoshihiro Abe, Marek Biskup, Sangchul Lee

Given a sequence of lattice approximations $D_{N} \subset Z^{2}$ of a bounded continuum domain $D \subset R^{2}$ with the vertices outside $D_{N}$ fused together into one bound…

math.PR2019★ 12 cited

Exceptional points of two-dimensional random walks at multiples of the cover time

Yoshihiro Abe, Marek Biskup

We study exceptional sets of the local time of the continuous-time simple random walk in scaled-up (by $N$ ) versions $D_{N} \subseteq Z^{2}$ of bounded open domains $D\subseteq…

math.PR2017★ 6 cited

Second order term of cover time for planar simple random walk

Yoshihiro Abe

We consider the cover time for a simple random walk on the two-dimensional discrete torus of side length $n$ . Dembo, Peres, Rosen, and Zeitouni [Ann. Math. 160:433-464, 2004] ident…

math.PR2016★ 4 cited

Extremes of local times for simple random walks on symmetric trees

Yoshihiro Abe

We consider local times of the simple random walk on the $b$ -ary tree of depth $n$ and study a point process which encodes the location of the vertex with the maximal local time an…

math.PR2014

Maximum and minimum of local times for two-dimensional random walk

Yoshihiro Abe

We obtain the leading orders of the maximum and the minimum of local times for the simple random walk on the two-dimensional torus at time proportional to the cover time. We also e…

math.PR2013★ 1 cited

Effective resistances for supercritical percolation clusters in boxes

Yoshihiro Abe

Let $C^{n}$ be the largest open cluster for supercritical Bernoulli bond percolation in $[- n, n]^{d} \cap Z^{d}$ with $d \geq 2$ . We obtain a sharp estimate for the eff…

math.PR2012★ 8 cited

Cover times for sequences of reversible Markov chains on random graphs

Yoshihiro Abe

We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (Type 1) is the class of cover times that are of the order o…