The hydrodynamic limit for a system with interactions prescribed by Ginzburg-Landau type random Hamiltonian
type: Item
instance of: scholarly article
title: The hydrodynamic limit for a system with interactions prescribed by Ginzburg-Landau type random Hamiltonian
zbMATH Open document ID: 0729.60105
DOI: 10.1007/BF01192142
author: Tadahisa Funaki
publication date: 1991-01-01T00:00:00Z
review text: As a microscopic model we consider a system of interacting continuum like spin field over \({\mathbb{R}}^ d\). Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scaling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4205584
zbMATH Keywords: law of large numbers for Gibbs states
zbMATH Keywords: microscopic model
zbMATH Keywords: system of interacting continuum
zbMATH Keywords: total spin of the system
zbMATH Keywords: hydrodynamic space-time scaling
zbMATH Keywords: hydrodynamic scaling
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4205584