一维简单随机游走无限频繁地出现三个喜欢的边缘

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-07-17 DOI:10.1007/s40304-023-00382-2

Chen-Xu Hao, Ze-Chun Hu, Ting Ma, Renming Song

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引用次数: 0

摘要

对于一维简单对称随机游走（(S_n)\），如果一条边 x（在点 \(x-1\) 和 x 之间）在 n 时刻的局部时间在所有边中达到最大，那么这条边 x 在 n 时刻被称为最爱边。在本文中，我们证明了在概率为 1 的情况下，三条最喜欢的边会无限频繁地出现。我们的工作受到 Tóth 和 Werner（Comb Probab Comput 6:359-369, 1997）以及 Ding 和 Shen（Ann Probab 46:2545-2561, 2018）的启发，推翻了 Tóth 和 Werner（1997）第 368 页备注 1 中提到的一个猜想。

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Three Favorite Edges Occurs Infinitely Often for One-Dimensional Simple Random Walk

For a one-dimensional simple symmetric random walk \((S_n)\), an edge x (between points \(x-1\) and x) is called a favorite edge at time n if its local time at n achieves the maximum among all edges. In this paper, we show that with probability 1 three favorite edges occurs infinitely often. Our work is inspired by Tóth and Werner (Comb Probab Comput 6:359–369, 1997), and Ding and Shen (Ann Probab 46:2545–2561, 2018), disproves a conjecture mentioned in Remark 1 on page 368 of Tóth and Werner (1997).

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.