### 抜粋

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^{-1}ΔP(ρ), where P is an increasing function which in a typical case equals const·ρ^{2}.

元の言語 | English |
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ページ（範囲） | 47-74 |

ページ数 | 28 |

ジャーナル | Probability Theory and Related Fields |

巻 | 95 |

発行部数 | 1 |

DOI | |

出版物ステータス | Published - 1993 3 1 |

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

## フィンガープリント Hydrodynamic limit for a spin system on a multidimensional lattice' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Probability Theory and Related Fields*,

*95*(1), 47-74. https://doi.org/10.1007/BF01197337