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November 2018 Exit time for a reaction diffusion model: Case of a one well potential
Adrian Hinojosa
Braz. J. Probab. Stat. 32(4): 783-794 (November 2018). DOI: 10.1214/17-BJPS363

Abstract

We consider a interacting particle system, the Glauber $+$ Kawasaki model. This model is the result of the combination of a fast stirring, the Kawasaki part, and a spin flip process, the Glauber part. This process has a Reaction–Diffusion equation as hydrodynamic limit, as is proven by De Masi and Presutti (Mathematical Methods for Hydrodynamic Limits (1991) Springer). The ergodicity of these dynamics (one well potential) was proven in Brasseco et al. (Amer. Math. Soc. Transl. Ser. 2 198 (2000) 37–49), for any dimension. In this article, we prove the asymptotic exponentiality for certain exit time from a subset of the basin of attraction of the well.

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Adrian Hinojosa. "Exit time for a reaction diffusion model: Case of a one well potential." Braz. J. Probab. Stat. 32 (4) 783 - 794, November 2018. https://doi.org/10.1214/17-BJPS363

Information

Received: 1 August 2015; Accepted: 1 April 2017; Published: November 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06979600
MathSciNet: MR3845029
Digital Object Identifier: 10.1214/17-BJPS363

Rights: Copyright © 2018 Brazilian Statistical Association

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Vol.32 • No. 4 • November 2018
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