Abstract
An anisotropic lattice gas dynamics is investigated for which particles on ℤd jump to empty nearest neighbor sites with (fast) rate ε−2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the “fast-rate” direction is rescaled by ε−1. It follows that the density field converges in probability, as ε↓0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (∼1/r d) with the direction dependence of a quadrupole field.
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Maes, C. Kinetic limit of a conservative lattice gas dynamics showing long-range correlations. J Stat Phys 61, 667–681 (1990). https://doi.org/10.1007/BF01027296
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DOI: https://doi.org/10.1007/BF01027296