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October 2001 The Branching Random Walk and Contact Process on Galton-Watson and Nonhomogeneous Trees
Robin Pemantle, Alan M. Stacey
Ann. Probab. 29(4): 1563-1590 (October 2001). DOI: 10.1214/aop/1015345762

Abstract

We show that the branching random walk on a Galton–Watson tree may have one or two phase transitions, depending on the relative sizes of the mean degree and the maximum degree. We show that there are some Galton–Watson trees on which the branching random walk has one phase transition while the contact process has two; this contradicts a conjecture of Madras and Schinazi. We show that the contact process has only one phase transition on some trees of uniformly exponential growth and bounded degree, contradicting a conjecture of Pemantle.

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Robin Pemantle. Alan M. Stacey. "The Branching Random Walk and Contact Process on Galton-Watson and Nonhomogeneous Trees." Ann. Probab. 29 (4) 1563 - 1590, October 2001. https://doi.org/10.1214/aop/1015345762

Information

Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1013.60078
MathSciNet: MR1880232
Digital Object Identifier: 10.1214/aop/1015345762

Subjects:
Primary: 60K35

Keywords: Branching random walk , contact process , phase transition , spectral radius , tree

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 4 • October 2001
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