Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process

TL;DR

This paper derives exact formulas for the transition probabilities of multi-species ASEP, expressing them as determinants under certain ordering conditions, advancing the mathematical understanding of these stochastic processes.

Contribution

The paper provides explicit determinant formulas for transition probabilities in multi-species ASEP, a novel result for these complex stochastic models.

Findings

Transition probabilities are expressed as determinants when initial and final particle orders match.

Explicit formulas are derived for the N-particle multi-species ASEP.

The results facilitate exact analysis of multi-species exclusion processes.

Abstract

We find the formulas of the transition probabilities of the $N$-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the final state is the same as the order of particles in the initial state.