## The Annals of Probability

### Gradient Dynamics of Infinite Point Systems

J. Fritz

#### Abstract

Nonequilibrium gradient dynamics of $d$-dimensional particle systems is investigated. The interaction is given by a superstable pair potential of finite range. Solutions are constructed in the well-defined set of locally finite configurations with a logarithmic order of energy fluctuations. If the system is deterministic and $d \leq 2$, then singular potentials are also allowed. For stochastic models with a smooth interaction we need $d \leq 4$. In order to develop some prerequisites for the theory of hydrodynamical fluctuations in equilibrium, we investigate smoothness of the Markov semigroup and describe some properties of its generator.

#### Article information

Source
Ann. Probab., Volume 15, Number 2 (1987), 478-514.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992156

Digital Object Identifier
doi:10.1214/aop/1176992156

Mathematical Reviews number (MathSciNet)
MR885128

Zentralblatt MATH identifier
0623.60119

JSTOR