Hydrodynamic limit for a spin system on a multidimensional lattice

Yuki Suzuki, Kôhei Uchiyama

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The hydrodynamic limit for a Markov process of [0, ∞)-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 thier 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 non-linear diffusion equation ∂ρ/∂t=2-1ΔP(ρ), where P is an increasing function which in a typical case equals const·ρ2.

Original languageEnglish
Pages (from-to)47-74
Number of pages28
JournalProbability Theory and Related Fields
Volume95
Issue number1
DOIs
Publication statusPublished - 1993 Mar

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Hydrodynamic Limit
Spin Systems
Energy Distribution
Energy
Nonlinear Diffusion Equation
Increasing Functions
Markov Process
Adjacent
Scaling
Gradient
Converge

Keywords

  • Mathematics Subject Classifications (1980): 60K35, 82A50

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

Hydrodynamic limit for a spin system on a multidimensional lattice. / Suzuki, Yuki; Uchiyama, Kôhei.

In: Probability Theory and Related Fields, Vol. 95, No. 1, 03.1993, p. 47-74.

Research output: Contribution to journalArticle

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