Noise sensitivity of random walks on groups

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2023-01-01 DOI:10.30757/alea.v20-42

Itaï Benjamini, Jérémie Brieussel

引用次数: 2

Abstract

A random walk on a group is noise sensitive if resampling every step independantly with a small probability results in an almost independant output. We precisely define two notions: $\ell^1$-noise sensitivity and entropy noise sensitivity. Groups with one of these properties are necessarily Liouville. Homomorphisms to free abelian groups provide an obstruction to $\ell^1$-noise sensitivity. We also provide examples of $\ell^1$ and entropy noise sensitive random walks.

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随机漫步对群体的噪声敏感性

如果以小概率独立地对每一步重新采样会产生几乎独立的输出，则对组上的随机漫步是噪声敏感的。我们精确地定义了两个概念:$\ well ^1$-噪声灵敏度和熵噪声灵敏度。具有这些性质之一的群必然是刘维尔群。自由阿贝尔群的同态对$\ell^1$-噪声灵敏度有阻碍作用。我们还提供了$\ well ^1$和熵噪声敏感随机漫步的例子。

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

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.