Second Class Particle Behaviour in Blocking ASEP

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.

43 pages, 4 figures. Accepted article. New introduction from previous version

References in corpus (8)

• Stationary distributions of multi-type totally asymmetric exclusion processes
• $q$-exchangeability via quasi-invariance
• Combinatorial Perspectives on the Crank and Mex Partition Statistics
• Joint distribution of Busemann functions in the exactly solvable corner growth model
• On the Distribution of a Second Class Particle in the Asymmetric Simple Exclusion Process
• Product blocking measures and a particle system proof of the Jacobi triple product
• Mallows Product Measure
• Interacting Particle Systems and Jacobi Style Identities

Cited by in corpus (1)

• Mallows Product Measure