Asymptotic Equivalence of Fluctuation Fields for Reversible Exclusion Processes with Speed Change

We consider stationary, reversible exclusion processes with speed change and prove that for sufficiently small interaction the fluctuation fields constructed from local functions become proportional to the density fluctuation field when averaged over suitably large space-time regions. If the exclusi...

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Bibliographic Details
Published in:The Annals of probability 1986-04, Vol.14 (2), p.409-423
Main Authors: De Masi, A., Presutti, E., Spohn, H., Wick, W. D.
Format: Article
Language:English
Subjects:
60F05
60K35
82A05
Central limit theorem
Cubes
Exact sciences and technology
Exclusion processes with speed change
infinite-dimensional Ornstein-Uhlenbeck processes
Ising model
linearized hydrodynamics
Mathematical functions
Mathematical theorems
Mathematics
Ornstein Uhlenbeck process
Particle interactions
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Semigroups
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Uniqueness
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Summary:We consider stationary, reversible exclusion processes with speed change and prove that for sufficiently small interaction the fluctuation fields constructed from local functions become proportional to the density fluctuation field when averaged over suitably large space-time regions. If the exclusion process is of gradient type, this result implies that the density fluctuation field converges to an infinite dimensional Ornstein-Uhlenbeck process.
ISSN:0091-1798
2168-894X
DOI:10.1214/aop/1176992524