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1 IME - Instituto de Matemática e Estatística

Abstract : We review some recent results for a system of simple random walks on graphs, known as \emphfrog model. Also, we discuss several modifications of this model, and present a few open problems. A simple version of the frog model can be described as follows: There are active and sleeping particles living on some graph. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1-p. When an active particle hits a sleeping particle, the latter becomes active.

Keywords : simple random walk critical probability shape theorem recurrence

Autor: Serguei Yu. Popov -



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