1302.5760 (Amir Dembo et al.)

Weakly Asymmetric Non-simple Exclusion Process and the KPZ equation    [PDF]

Amir Dembo, Li-Cheng Tsai

We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing the Gaertner transformation. While the original argument, which matches three identities with three parameters, applies only to simple exclusion process, our approach is to identify the major non-linear drift term of the microscopic dynamical equation and to convert the drift term into a quasi-linear second order differential, yielding the stochastic heat equation (SHE) in the continuum limit. Using the generalized transformation, we prove convergence toward the KPZ equation, which is the first universality result of this kind in the context of KPZ universality class. While this class of exclusion processes are not explicitly solvable, we obtain the exact one-point limit distribution for the step and step Bernoulli initial conditions by using the previous results of Amir et al. (2011), Corwin & Quastel (2010), and our convergence result.

View original: http://arxiv.org/abs/1302.5760