Fires on large recursive trees

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Marzouk, Cyril¹ 

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

关键词: Random recursive trees;    Fire model;    Percolation;    Cluster sizes;   

DOI  :  10.1016/j.spa.2015.08.006

来源: Elsevier

【 摘 要 】

We consider random dynamics on a uniform random recursive tree with n vertices. Successively, in a uniform random order, each edge is either set on fire with some probability p(n) or fireproof with probability 1 - p(n). Fires propagate in the tree and are only stopped by fireproof edges. We first consider the proportion of burnt and fireproof vertices as n -> infinity, and prove a phase transition when p(n) is of order 1n n/n. We then study the connectivity of the fireproof forest, more precisely the existence of a giant component. We finally investigate the sizes of the burnt subtrees. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free