The Annals of Probability

Gradient Dynamics of Infinite Point Systems

J. Fritz

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Keywords
Interacting Brownian particles superstable potentials generators of semigroups cores and essential self-adjointness

Citation

Fritz, J. Gradient Dynamics of Infinite Point Systems. Ann. Probab. 15 (1987), no. 2, 478--514. doi:10.1214/aop/1176992156. https://projecteuclid.org/euclid.aop/1176992156


Export citation