ASEP(q,j) converges to the KPZ equation
  We show that a generalized Asymmetric Exclusion Process called ASEP(q,j) introduced by Carinci, Giardina, Redig and Sasamoto converges to the Cole-Hopf solution to the KPZ equation under weak asymmetry scaling. 
Ivan Corwin, Hao Shen, Li-Cheng Tsai
math.PR math-ph math.MP