Pfaffian Transition Probability and Correlation Kernel of TASEP in Half-space

TL;DR

This paper derives Pfaffian formulas for transition probabilities and multipoint distributions of TASEP in half-space, revealing new connections with Pfaffian point processes and simplifying the analysis of the model.

Contribution

It introduces a Pfaffian transition probability and a Fredholm Pfaffian formula for TASEP in half-space, extending understanding of its probabilistic structure.

Findings

Transition probability reduces to a Pfaffian in the totally asymmetric limit.

Derived a Fredholm Pfaffian formula for multipoint distributions.

Connected TASEP with Pfaffian point processes on Gelfand-Tsetlin patterns.

Abstract

We present the transition probability for the asymmetric simple exclusion process on the half-space for general initial conditions and particle insertion at the boundary. In the limit of total asymmetry, where particles only jump to the right, we show that the transition probability reduces to a single Pfaffian for a large class of initial conditions. We further derive a Fredholm Pfaffian formula for the multipoint distribution of the totally asymmetric model conditioned on the number of particles in the system using a connection with a Pfaffian point process supported on Gelfand-Tsetlin patterns.