Equilibrium fluctuations for a nongradient energy conserving stochastic model

Details Equilibrium fluctuations for a nongradient energy conserving stochastic model Equilibrium fluctuations for a nongradient energy conserving stochastic model

2010-06-30

arxiv.org/abs/1006.5861v1

Mathematics

Probability

41 pages

Scientific paper

In this paper we study the equilibrium energy fluctuation field of a one-dimensional reversible non gradient model. We prove that the limit fluctuation process is governed by a generalized Ornstein- Uhlenbeck process, which covariances are given in terms of the diffusion coefficient. Adapting the non gradient method introduced by Varadhan, we are able to derive the diffusion coefficient. The fact that the conserved quantity (energy) is not a linear functional of the coordinates of the system, introduces new difficulties of geometric nature when applying the nongradient method.

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