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.
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Received: 3 October 1996 / Accepted: 13 February 1997
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Carmona, R., Xu, L. Diffusive Hydrodynamic Limits for Systems of Interacting Diffusions with Finite Range Random Interaction . Comm Math Phys 188, 565–584 (1997). https://doi.org/10.1007/s002200050179
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DOI: https://doi.org/10.1007/s002200050179