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October, 1988 The Contact Process on a Finite Set. II
Richard Durrett, Roberto H. Schonmann
Ann. Probab. 16(4): 1570-1583 (October, 1988). DOI: 10.1214/aop/1176991584


In this paper we complete the work started in part I. We show that if $\sigma_N$ is the time that the contact process on $\{1,\ldots, N\}$ first hits the empty set, then for $\lambda > \lambda_c$ (the critical value for the process on $Z$) there is a positive constant $\gamma(\lambda)$ so that $(\log \sigma_N)/N\rightarrow\gamma(\lambda)$ in probability as $N\rightarrow\infty$. We also give a new simple proof that $\sigma_N/E\sigma_N$ converges to a mean one exponential. The keys to the proof of the first result are a "planar graph duality" for the contact process and an observation of J. Chayes and L. Chayes that exponential decay rates for connections in strips approach the decay rates in the plane as the width of the strip goes to $\infty$.


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Richard Durrett. Roberto H. Schonmann. "The Contact Process on a Finite Set. II." Ann. Probab. 16 (4) 1570 - 1583, October, 1988.


Published: October, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0664.60106
MathSciNet: MR958203
Digital Object Identifier: 10.1214/aop/1176991584

Primary: 60K35

Keywords: Biased voter model , contact process

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 4 • October, 1988
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