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January, 1992 Brownian Fluctuations of the Edge for Critical Reversible Nearest-Particle Systems
Rinaldo Schinazi
Ann. Probab. 20(1): 194-205 (January, 1992). DOI: 10.1214/aop/1176989924


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.


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Rinaldo Schinazi. "Brownian Fluctuations of the Edge for Critical Reversible Nearest-Particle Systems." Ann. Probab. 20 (1) 194 - 205, January, 1992.


Published: January, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0742.60108
MathSciNet: MR1143418
Digital Object Identifier: 10.1214/aop/1176989924

Primary: 60K35

Keywords: edge fluctuations , infinite particle systems , reversible nearest-particle systems

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 1 • January, 1992
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