## Brazilian Journal of Probability and Statistics

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

### 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**

Received: August 2015

Accepted: April 2017

First available in Project Euclid: 17 August 2018

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/17-BJPS363

**Mathematical Reviews number (MathSciNet)**

MR3845029

**Zentralblatt MATH identifier**

06979600

**Keywords**

Exit times interacting particle systems Glauber–Kawasaki dynamics reaction–diffusion equations hydrodynamic limits

#### 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