Georgia Institute of Technology College of Sciences

The asymmetric simple exclusion process (ASEP) is a continuous time Markov process of interacting particles on a lattice \Gamma. ASEP is defined by two rules: (1) A particle at x \in \Gamma waits an exponential time with parameter one, and then chooses y \in \Gamma with probability p(x, y); (2) If y is vacant at that time it moves to y, while if y is occupied it remains at x. The main interest lies in infinite particle systems. In this lecture we consider the ASEP on the integer lattice {\mathbb Z} with nearest neighbor jump rule: p(x, x+1) = p, p(x, x-1) = 1-p and p \ne 1/2. The integrable structure is that of Bethe Ansatz. We discuss various limit theorems which in certain cases establishes KPZ universality.