在一棵大的凯莱树上燃烧和防火部件的大小

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2013-10-21 DOI:10.1214/14-AIHP640

Cyril Marzouk

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引用次数: 2

摘要

我们继续Jean Bertoin在2012年对具有$n$顶点的均匀Cayley树的边的随机动力学的研究，其中每条边依次以固定概率$p_n$着火或以概率$1-p_n$防火。被点燃的边缘燃烧并点燃其易燃的邻居，然后火焰在树木中传播，只有防火边缘才能阻止。根据$p_n$的渐近性，我们研究了燃烧和防火顶点的比例分布以及燃烧或防火连接分量的大小$n \to \infty$。

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On the sizes of burnt and fireproof components for fires on a large Cayley tree

We continue the study initiated by Jean Bertoin in 2012 of a random dynamics on the edges of a uniform Cayley tree with $n$ vertices in which, successively, each edge is either set on fire with some fixed probability $p_n$ or fireproof with probability $1-p_n$. An edge which is set on fire burns and sets on fire its flammable neighbors, the fire then propagates in the tree, only stopped by fireproof edges. We study the distribution of the proportion of burnt and fireproof vertices and the sizes of the burnt or fireproof connected components as $n \to \infty$ regarding the asymptotic behavior of $p_n$.

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来源期刊

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.