Diffusive hydrodynamic limits for systems of interacting diffusions with finite range random interaction

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Abstract

We consider a system of interacting diffusive particles with finite range random interaction. The variables can be interpreted as charges at sites indexed by a periodic multidimensional lattice. The equilibrium states of the system are canonical Gibbs measures with finite range random interaction. Under the diffusive scaling of lattice spacing and time, we derive a deterministic nonlinear diffusion equation for the time evolution of the macroscopic charge density. This limit is almost sure with respect to the random environment.

Original languageEnglish (US)
Pages (from-to)565-584
Number of pages20
JournalCommunications In Mathematical Physics
Volume188
Issue number3
DOIs
StatePublished - Jan 1 1997

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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