Equilibrium Fluctuations for Lattice Gases

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dc.creatorBenois, O.
dc.creatorEsposito, R.
dc.creatorMarra, R.
dc.date2000-12-26
dc.date.accessioned2026-07-07T04:28:13Z
dc.date.available2026-07-07T04:28:13Z
dc.descriptionThe authors in a previous paper proved the hydrodynamic incompressible limit in $d\ge 3$ for a thermal lattice gas, namely a law of large numbers for the density, velocity field and energy. In this paper the equilibrium fluctuations for this model are studied and a central limit theorem is proved for a suitable modification of the vector fluctuation field $\z(t)$, whose components are the density, velocity and energy fluctuations fields. We consider a modified fluctuation field $ξ^\e(t)=\exp \{-\ve^{-1}t E\}\z^\ve$, where $E$ is the linearized Euler operator around the equilibrium and prove that $ξ^\e(t)$ converges to a vector generalized Ornstein-Uhlenbeck process $ξ(t)$, which is formally solution of the stochastic differential equation $d ξ(t)=Nξ(t)dt+ B dW_t$, with $ BB^*=-2 NC$, where $C$ is the compressibility matrix, $N$ is a matrix whose entries are second order differential operators and $B$ is a mean zero Gaussian field. The relation $-2NC=BB^*$ is the fluctuation-dissipation relation.
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0012043
dc.identifierhttp://arxiv.org/abs/math-ph/0012043
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56707
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject60K35, 82C22
dc.titleEquilibrium Fluctuations for Lattice Gases
dc.typetext

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