The upper tail problem for induced 4‐cycles in sparse random graphs

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2023-10-16 DOI:10.1002/rsa.21187

Asaf Cohen Antonir

引用次数: 3

Abstract

Abstract Building on the techniques from the breakthrough paper of Harel, Mousset and Samotij, which solved the upper tail problem for cliques, we compute the asymptotics of the upper tail for the number of induced copies of the 4‐cycle in the binomial random graph . We observe a new phenomenon in the theory of large deviations of subgraph counts. This phenomenon is that, in a certain (large) range of , the upper tail of the induced 4‐cycle does not admit a naive mean‐field approximation.

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稀疏随机图中诱导4 -环的上尾问题

摘要:在Harel, Mousset和Samotij的突破性论文中解决了团的上尾问题的基础上，我们计算了二项随机图中4 -环的诱导拷贝数的上尾渐近性。在子图计数大偏差理论中，我们观察到一个新现象。这种现象是，在一定(大)范围内，诱导的4周期的上尾不允许朴素平均场近似。

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

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.