Second Class Particle Behaviour in Blocking ASEP

Key Points

• This research aims to analyze the behavior of second class particles in the asymmetric simple exclusion process and establish key probabilistic distributions.
• Constructed a basic coupling of two asymmetric simple exclusion processes (ASEPs) to explore particle behavior.
• Derived the joint distribution of second class particle positions and their probabilities at specific sites.
• Utilized results on particle counts in half-infinite and finite ranges of ASEP.
• Provided the joint distribution of second class particles under the blocking measure of ASEP.
• Established probabilities for the presence of second class particles at given sites.
• Confirmed probabilistic proofs of several combinatorial identities, including the Durfee rectangles identity and Euler's identity.

Abstract