Expected hitting time estimates on finite graphs

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-03-11 DOI:10.1016/j.spa.2025.104626

Laurent Saloff-Coste , Yuwen Wang

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引用次数: 0

Abstract

The expected hitting time from vertex

a

to vertex

b

H (a, b)

, is the expected value of the time it takes a random walk starting at

a

to reach

b

. In this paper, we give estimates for

H (a, b)

when the distance between

a

and

b

is comparable to the diameter of the graph, and the graph satisfies a Harnack condition. We show that, in such cases,

H (a, b)

can be estimated in terms of the volumes of balls around

b

. Using our results, we estimate

H (a, b)

on various graphs, such as rectangular tori, some convex traces in

Z^{d}

, and fractal graphs. Our proofs use heat kernel estimates.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.