Fires on large recursive trees

Cyril Marzouk

Stochastic Processes and their Applications, 2016, vol. 126, issue 1, 265-289

Abstract: 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 pn or fireproof with probability 1−pn. Fires propagate in the tree and are only stopped by fireproof edges. We first consider the proportion of burnt and fireproof vertices as n→∞, and prove a phase transition when pn is of order lnn/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.

Keywords: Random recursive trees; Fire model; Percolation; Cluster sizes (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.08.006

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