具有对称各向同性阈值规则的二维引导渗流的尖锐蜕变

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields Pub Date : 2024-08-21 DOI:10.1007/s00440-024-01310-3

Hugo Duminil-Copin, Ivailo Hartarsky

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引用次数: 0

摘要

我们研究了二维临界引导渗流模型。我们发现，这些模型中的一类，包括所有具有凸对称邻域的各向同性阈值规则，都会发生急剧的蜕变。这扩展了之前针对几种特定规则证明的实例。本文取代了亚历山大-霍尔罗伊德和第一作者在 2012 年的草稿。虽然它在引导式渗流普遍性的后续发展中发挥了作用，但我们还是选择以现在的形式采用更现代的观点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules

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Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules

We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourhood, undergoes a sharp metastability transition. This extends previous instances proved for several specific rules. The paper supersedes a draft by Alexander Holroyd and the first author from 2012. While it served a role in the subsequent development of bootstrap percolation universality, we have chosen to adopt a more contemporary viewpoint in its present form.

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.