Asymmetric simple exclusion process

In probability theory, the asymmetric simple exclusion process (ASEP) is an interacting particle system introduced in 1970 by Frank Spitzer in Interaction of Markov Processes. 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".

The process with parameters ${\displaystyle p,q\geqslant 0,\,p+q=1}$ is a continuous-time Markov process on ${\displaystyle S=\lbrace 0,1\rbrace ^{\mathbb {Z} }}$, the 1s being thought of as particles and the 0s as holes. Each particle waits a random exponent mean one amount of time and then attempts a jump, one site to the right with probability ${\displaystyle p}$ and one site to the left with probability ${\displaystyle q}$. However, the jump is performed only if there is no particle at the target site. Otherwise, nothing happens and the particle waits another exponential time. All particles are doing this independently of each other.

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