阿贝尔网络的本质改进:连续性和一致严格单调性

IF 2.1 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Probability Pub Date : 2023-01-01 DOI:10.1214/23-aop1647

Lorenzo Taggi

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引用次数: 5

摘要

在广义上证明了激活随机漫步模型的临界曲线是失活率的连续函数，并给出了其斜率的一个界，该界对于图的选择是一致的。此外，我们导出了一类“递增”事件的概率的严格单调性，扩展了(Invent)的先前结果。数学。188(2012)127-150)。我们的证明方法是独立的，可以看作是“基本增强”技术的重新表述，该技术是在阿贝尔网络框架中为渗透引入的。

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Essential enhancements in Abelian networks: Continuity and uniform strict monotonicity

We prove that in wide generality the critical curve of the activated random walk model is a continuous function of the deactivation rate, and we provide a bound on its slope, which is uniform with respect to the choice of the graph. Moreover, we derive strict monotonicity properties for the probability of a wide class of “increasing” events, extending previous results of (Invent. Math. 188 (2012) 127–150). Our proof method is of independent interest and can be viewed as a reformulation of the ‘essential enhancements’ technique, which was introduced for percolation, in the framework of abelian networks.

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来源期刊

Annals of Probability 数学-统计学与概率论

CiteScore

4.60

自引率

8.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Annals of Probability publishes research papers in modern probability theory, its relations to other areas of mathematics, and its applications in the physical and biological sciences. Emphasis is on importance, interest, and originality – formal novelty and correctness are not sufficient for publication. The Annals will also publish authoritative review papers and surveys of areas in vigorous development.