On Pólya’s random walk constants

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-04-19 DOI:10.1090/proc/16854

Robert Gaunt, Saralees Nadarajah, Tibor Pogány

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引用次数: 0

Abstract

A celebrated result in probability theory is that a simple symmetric random walk on the d d -dimensional lattice Z d \mathbb {Z}^d is recurrent for d = 1 , 2 d=1,2 and transient for d ≥ 3 d\geq 3 . In this note, we derive a closed-form expression, in terms of the Lauricella function F C F_C , for the return probability for all d ≥ 3 d\geq 3 . Previously, a closed-form formula had only been available for d = 3 d=3 .

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关于 Pólya 的随机行走常数

概率论中一个著名的结果是，在 d d 维网格 Z d \mathbb {Z}^d 上的简单对称随机行走在 d = 1 , 2 d=1,2 时是经常性的，而在 d ≥ 3 d\geq 3 时是瞬时性的。在本说明中，我们用劳里切拉函数 F C F_C 为所有 d ≥ 3 d\geq 3 的回归概率推导出一个闭式表达式。在此之前，只有 d=3 d=3 时才有闭式公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

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