## The Annals of Probability

- Ann. Probab.
- Volume 19, Number 4 (1991), 1537-1558.

### Hydrodynamical Equation for Attractive Particle Systems on $\mathbb{Z}^d$

#### Abstract

We prove conservation of local equilibrium, away from the shock, for some attractive asymmetric particle systems on $\mathbb{Z}^d$. The method applies to a class of particle processes which includes zero-range and simple exclusion processes. The main point in the proof is to exploit attractiveness. The hydrodynamic equation obtained is a first-order nonlinear partial differential equation which presents shock waves.

#### Article information

**Source**

Ann. Probab., Volume 19, Number 4 (1991), 1537-1558.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176990222

**Digital Object Identifier**

doi:10.1214/aop/1176990222

**Mathematical Reviews number (MathSciNet)**

MR1127714

**Zentralblatt MATH identifier**

0798.60084

**JSTOR**

links.jstor.org

**Subjects**

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

**Keywords**

Infinite particle systems hydrodynamical equations asymmetric zero range process

#### Citation

Landim, C. Hydrodynamical Equation for Attractive Particle Systems on $\mathbb{Z}^d$. Ann. Probab. 19 (1991), no. 4, 1537--1558. doi:10.1214/aop/1176990222. https://projecteuclid.org/euclid.aop/1176990222