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April, 1987 Gradient Dynamics of Infinite Point Systems
J. Fritz
Ann. Probab. 15(2): 478-514 (April, 1987). DOI: 10.1214/aop/1176992156


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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J. Fritz. "Gradient Dynamics of Infinite Point Systems." Ann. Probab. 15 (2) 478 - 514, April, 1987.


Published: April, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0623.60119
MathSciNet: MR885128
Digital Object Identifier: 10.1214/aop/1176992156

Primary: 60K35
Secondary: 60H10 , 60J35

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

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 2 • April, 1987
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