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July, 1987 Edge Fluctuations for the One Dimensional Supercritical Contact Process
Antonio Galves, Errico Presutti
Ann. Probab. 15(3): 1131-1145 (July, 1987). DOI: 10.1214/aop/1176992086

Abstract

We consider the one dimensional supercritical contact process with initial configurations having infinitely many particles to the left of the origin and only finitely many to its right. Starting from any such configuration, we first prove that in the limit as time goes to infinity the law of the process, as seen from the edge, converges to the invariant distribution constructed by Durrett [12]. We then prove a functional central limit theorem for the fluctuations of the edge around its average, showing that the corresponding diffusion coefficient is strictly positive. We finally characterize the space time structure of the system. In particular we prove that its distribution shifted in space by $\alpha t$ ($t$ denotes the time and $\alpha$ the drift of the edge) converges when $t$ goes to infinity to a $\frac{1}{2} - \frac{1}{2}$ mixture of the two extremal invariant measures for the contact process.

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Antonio Galves. Errico Presutti. "Edge Fluctuations for the One Dimensional Supercritical Contact Process." Ann. Probab. 15 (3) 1131 - 1145, July, 1987. https://doi.org/10.1214/aop/1176992086

Information

Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0645.60103
MathSciNet: MR893919
Digital Object Identifier: 10.1214/aop/1176992086

Subjects:
Primary: 60K35

Keywords: contact process , edge fluctuations , invariance principle

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • July, 1987
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