## Brazilian Journal of Probability and Statistics

### Exit time for a reaction diffusion model: Case of a one well potential

#### 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.

#### Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 4 (2018), 783-794.

Dates
Accepted: April 2017
First available in Project Euclid: 17 August 2018

https://projecteuclid.org/euclid.bjps/1534492901

Digital Object Identifier
doi:10.1214/17-BJPS363

Mathematical Reviews number (MathSciNet)
MR3845029

Zentralblatt MATH identifier
06979600

#### Citation

Hinojosa, Adrian. Exit time for a reaction diffusion model: Case of a one well potential. Braz. J. Probab. Stat. 32 (2018), no. 4, 783--794. doi:10.1214/17-BJPS363. https://projecteuclid.org/euclid.bjps/1534492901

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