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January 2000 Critical exponents for a reversible nearest particle system on the binary tree
Amber L. Puha
Ann. Probab. 28(1): 395-415 (January 2000). DOI: 10.1214/aop/1019160124


The uniform model is a reversible interactingparticle system that evolves on the homogeneous tree. Occupied sites become vacant at rate one provided the number of occupied neighbors does not exceed one.Vacant sites become occupied at rate $\beta$ times the number of occupied neighbors. On the binary tree, it has been shown that the survival threshold $\beta_c$ is 1/4. In particular, for $\beta \leq 1/4$, the expected extinction time is finite.Otherwise, the uniform model survives locally. We show that the survival probability decays faster than a quadratic near $\beta_c$. This contrasts with the behavior of the survival probability for the contact process on homogeneous trees, which decays linearly.We also provide a lower bound that implies that the rate of decay is slower than a cubic. Tools associated with reversibility, for example, the Dirichlet principle and Thompson's principle, are used to prove this result.


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Amber L. Puha. "Critical exponents for a reversible nearest particle system on the binary tree." Ann. Probab. 28 (1) 395 - 415, January 2000.


Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60097
MathSciNet: MR1756010
Digital Object Identifier: 10.1214/aop/1019160124

Primary: 60K35 , 82O22

Keywords: Critical exponents , growth models , phase transition , reversible flows , trees

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 1 • January 2000
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