The Annals of Probability
- Ann. Probab.
- Volume 15, Number 2 (1987), 478-514.
Gradient Dynamics of Infinite Point Systems
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.
Ann. Probab., Volume 15, Number 2 (1987), 478-514.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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