Density of random subsets and applications to group theory

Tsai Tsung-Hsuan

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Density of random subsets and applications to group theory

机译：随机子集的密度及其在群论中的应用

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Developing an idea of M. Gromov (1993), we study the intersection formula for random subsets with density. The density of a subset A in a finite set E is defined by dens A := log(|E|)(|A|). The aim of this article is to give a precise meaning of Gromov's intersection formula: "Random subsets" A and B of a finite set E satisfy dens(A boolean AND B) = densA + densB - 1. As an application, we exhibit a phase transition phenomenon for random presentations of groups at density lambda/2 for any 0 < lambda < 1, characterizing the C' (lambda)-small cancellation condition. We also improve an important result of random groups by G. Arzhantseva and A. Ol'shanskii (1996) from density 0 to density 0 <= d < 1/ (120m(2) ln(2m))

机译：开发一个m .格罗莫夫(1993),我们的研究十字路口的公式随机子集密度。集E是由洞穴:=日志(| | E)(| |)。本文的目的是给出一个精确的意义格罗莫夫交集的公式:“随机的有限集的子集”A和B E满足洞穴(A布尔和B) = densA + densB - 1。应用程序中,我们表现出相变现象为随机演示组密度λ/ 2为任何0 <λ< 1,描述C”(λ),取消非同寻常条件。g . Arzhantseva和随机的组。Ol 'shanskii密度(1996)从密度0到0 < =d < 1 /(120米(2)ln(2米))

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《Journal of combinatorial algebra》 |2022年第4期|223-263|共41页
作者
Tsai Tsung-Hsuan;
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Inst Rech Math Avancee;

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原文格式 PDF
正文语种英语
中图分类数学;
关键词
Random group; intersection formula; cancellation theory; SUBGROUPS; PROPERTY;

机译：随机组;交集公式;取消理论;子组;财产;

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Density of random subsets and applications to group theory

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