Branching random walks on trees

Neal Madras and Rinaldo Schinazi

Stochastic Processes and their Applications, 1992, vol. 42, issue 2, 255-267

Abstract: Let p(x, y) be the transition probability of an isotropic random walk on a tree, where each site has d [greater-or-equal, slanted]3 neighbors. We define a branching random walk by letting a particle at site x give birth to a new particle at site y at rate [lambda]dp(x, y), jump to y at rate vdp(x, y), and die at rate [delta]. Let [lambda]2 (respectively, [mu]2) be the infimum of [lambda] such that the process starting with one particle has positive probability of surviving forever (respectively, of having a fixed site occupied at arbitrarily large times). We compute [lambda]2 and [mu]2 exactly, proving that [lambda]2

Keywords: branching; random; walk; tree; biased; voter; model; contact; process; phase; transition (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (2)

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