Hydrodynamic limit for a spin system on a multidimensional lattice

Yuki suzuki, Kôhei Uchiyama

研究成果: Article査読

10 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)47-74
ページ数28
ジャーナルProbability Theory and Related Fields
95
1
DOI
出版ステータスPublished - 1993 3月

ASJC Scopus subject areas

  • 分析
  • 統計学および確率
  • 統計学、確率および不確実性

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