亚临界单调元胞自动机

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2022-03-03 DOI:10.1002/rsa.21174

P. Balister, B. Bollob'as, R. Morris, Paul Smith

引用次数: 3

摘要

我们研究了$\mathbb{Z}^d$中具有随机初始配置的单调元胞自动机(也称为$\mathcal{U}$-bootstrap渗流)。我们证实了Balister、Bollob\ as、Przykucki和Smith在二维上证明了相应结果的一个猜想，证明了所有亚临界模型的临界概率不为零。

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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Subcritical monotone cellular automata

We study monotone cellular automata (also known as $\mathcal{U}$-bootstrap percolation) in $\mathbb{Z}^d$ with random initial configurations. Confirming a conjecture of Balister, Bollob\'as, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non-zero for all subcritical models.

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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.