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26 April 2024
 
  » arxiv » 1606.6655

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Stochastic Burgers equation from long range exclusion interactions
Patricia Gonçalves ; Milton Jara ;
Date 21 Jun 2016
AbstractWe consider one-dimensional exclusion processes with long jumps given by a transition probability of the form $p_n(cdot)=s(cdot)+gamma_na(cdot)$, such that its symmetric part $s(cdot)$ is irreducible with finite variance and its antisymmetric part is absolutely bounded by $s(cdot).$ We prove that under diffusive time scaling and strength of asymmetry $sqrt n gamma_n o_{n oinfty} b eq 0$, the equilibrium density fluctuations are given by the unique energy solution of the stochastic Burgers equation.
Source arXiv, 1606.6655
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