In probability theory, the asymmetric simple exclusion process (ASEP) is an interacting particle system introduced in 1970 by Frank Spitzer.
[1] Many articles have been published on it in the physics and mathematics literature since then, and it has become a "default stochastic model for transport phenomena".
Each particle waits a random amount of time having the distribution of an exponential random variable with mean one and then attempts a jump, one site to the right with probability
The model is related to the Kardar–Parisi–Zhang equation in the weakly asymmetric limit, i.e. when
Recently, progress has been made to understand the statistics of the current of particles and it appears that the Tracy–Widom distribution plays a key role.