Stochastic Burgers equation from long range exclusion interactions
Abstract
We consider onedimensional 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 $\sqrt n \gamma_n \to_{n\to\infty} b\neq 0$, the equilibrium density fluctuations are given by the unique energy solution of the stochastic Burgers equation.
 Publication:

arXiv eprints
 Pub Date:
 June 2016
 arXiv:
 arXiv:1606.06655
 Bibcode:
 2016arXiv160606655G
 Keywords:

 Mathematics  Probability;
 60K35
 EPrint:
 22 pages