Hydrodynamic limit for a spin system on a multidimensional lattice
type: Item
instance of: scholarly article
title: Hydrodynamic limit for a spin system on a multidimensional lattice
zbMATH Open document ID: 0794.60099
DOI: 10.1007/BF01197337
author: Yuki Suzuki
author: Kohei Uchiyama
publication date: 1994-08-15T00:00:00Z
review text: The hydrodynamic limit for a Markov process of \([0,\infty)\)-valued spin fields on a periodic multidimensional lattice is studied. In the process a positive real number, called energy, is attached to each site of the lattice and each couple of adjacent sites exchange their energy by random amounts at random times. The law of the exchange is such that the sum of the total energy is conserved, and that the process is reversible and of gradient type for the energy distribution. We show that under diffusion type scaling of space and time, the macroscopic energy distribution converges to a deterministic limit which is characterized by a nonlinear diffusion equation \(\partial \rho/ \partial t=2^{-1} \Delta P (\rho)\), where \(P\) is an increasing function which in a typical case equals \(\text{const} \cdot \rho^ 2\).
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 569038
zbMATH Keywords: hydrodynamic limit
zbMATH Keywords: spin fields
zbMATH Keywords: periodic multidimensional lattice
zbMATH Keywords: random times
zbMATH Keywords: macroscopic energy distribution
MaRDI profile type: Publication
cites work: Q5560061
cites work: Nonlinear diffusion limit for a system with nearest neighbor interactions
cites work: Scaling limits for interacting diffusions
full work available at URL: https://doi.org/10.1007/bf01197337
OpenAlex ID: W1979559193
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569038