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对有限图的预期命中时间估计

IF 1.2 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

摘要

从点a到点b的期望命中时间H（a,b）是从点a开始随机行走到达点b所需时间的期望值。本文给出了当点a与点b之间的距离与图的直径相当，且图满足Harnack条件时H（a,b）的估计。我们证明，在这种情况下，H（a,b）可以根据b周围的球的体积来估计。使用我们的结果，我们可以在各种图上估计H(a,b)，例如矩形环面，Zd中的一些凸迹和分形图。我们的证明使用热核估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Expected hitting time estimates on finite graphs

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.