Hydrodynamics and large deviation for simple exclusion processes. (English) Zbl 0644.76001

We prove the hydrodynamical limit for weakly asymmetric simple exclusion processes. A large deviation property with respect to this limit is established for the symmetric case. We treat also the situation where a slow reaction (creation and annihilation of particles) is present.
Reviewer: C.Kipnis


76A02 Foundations of fluid mechanics
82B05 Classical equilibrium statistical mechanics (general)
76M99 Basic methods in fluid mechanics
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[1] Dawson, Stochastics 20 pp 247– (1987) · Zbl 0613.60021
[2] DeMasi, J. Stat. Phys. 44 pp 589– (1986)
[3] , , and , A survey of the hydrodynamical behavior of many particle systems, Studies in Statistical Mechanics 11, and , eds., North-Holland, 1984, pp. 123–294.
[4] , and , The Weakly Asymmetric Simple Exclusion Processes, CARR Reports in Mathematical Physics, 1987.
[5] Donsker, Comm. Pure Appl. Math 42 (1989)
[6] Gartner, Stochastic Processes and their Applications 27 pp 233– (1988)
[7] and , Large deviations from the hydrodynamical limit for a system of independent Brownian particles, to appear in Stochastics. · Zbl 0734.60099
[8] Papanicolaou, Comm. Math. Phys. 118 pp 31– (1988)
[9] Large Deviations and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics 46, Philadelphia, Society for Industrial and Applied Mathematics, 1984.
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