Second Class Particle Behaviour in Blocking ASEP

Adams, Daniel and Balázs, Márton and Jay, Jessica (2026) Second Class Particle Behaviour in Blocking ASEP. Latin American Journal of Probability and Mathematical Statistics. ISSN 1980-0436 (In Press)

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Abstract

We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second class particles and also the probability of there being a second class particle at a given site, under the natural blocking measure for ASEP. In order to find these distributions we use results about the number of particles in half-infinite and finite site ranges of ASEP. Our investigations also lead to probabilistic proofs of well-known combinatorial identities; the Durfee rectangles identity, Euler's identity, and the $q$-Binomial Theorem.