Second Class Particle Behaviour in Blocking ASEP

We consider any fixed d 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.