The Annals of Probability

Brownian Fluctuations of the Edge for Critical Reversible Nearest-Particle Systems

Rinaldo Schinazi

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We apply an invariance principle due to De Masi, Ferrari, Goldstein and Wick to the edge process for critical reversible nearest-particle systems. Their result also gives an upper bound for the diffusion constant that we compute explicitly. A comparison between the movement of the edge, when the other particles are frozen, and a random walk allows us to find a lower bound for the diffusion constant. This shows that the right renormalization for the edge to converge to a nondegenerate Brownian motion is the usual one. Note that analogous results for nearest-particle systems are only known for the contact process in the supercritical case.

Article information

Ann. Probab., Volume 20, Number 1 (1992), 194-205.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Infinite particle systems reversible nearest-particle systems edge fluctuations


Schinazi, Rinaldo. Brownian Fluctuations of the Edge for Critical Reversible Nearest-Particle Systems. Ann. Probab. 20 (1992), no. 1, 194--205. doi:10.1214/aop/1176989924.

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