The Annals of Probability

Gradient Dynamics of Infinite Point Systems

J. Fritz

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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.

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

First available in Project Euclid: 19 April 2007

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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]

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


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

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