 95451 L. Bertini, G. Giacomin
 Stochastic Burgers and KPZ equations from particle systems
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Oct 12, 95

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Abstract. We consider the weakly asymmetric exclusion process
on the one dimensional lattice. It has been proven that,
in the diffusive scaling limit, the density field evolves
according to the Burgers equation and the fluctuation field
converges to a generalized OrnsteinUhlenbeck process.
We analyze instead the density fluctuations beyond the
hydrodynamical scale and prove that their limiting distribution
solves the (non linear) Burgers equation with a random noise
on the density current.
We also study an interface growth model, for which the
microscopic dynamics is a SolidOnSolid type deposition process.
We prove that the fluctuation field, if suitably rescaled,
converges to the KardarParisiZhang equation. This provides
a microscopic justification of the so called {\em kinetical roughening},
i.e.the non Gaussian fluctuations in some nonequilibrium processes.
Our main tool is the ColeHopf transformation and its microscopic
version. We also exploit the (known) connection between the two
microscopic models and develop a mathematical theory for the
macroscopic equations.
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