EXTENSION OF TRANSITION PROBABILITY FORMULAS IN MULTI-SPECIES ASYMMETRIC SIMPLE EXCLUSION PROCESS

Abstract

The Asymmetric Simple Exclusion Process (ASEP) is a mathematical model used to describe the movement of particles in a one-dimensional system. This work explores multi-species ASEP dynamics, where, in contrast to the single-species model, additional rules regulate interactions between various particle kinds. Tracy and Widom introduced a transition probability formula for single-species ASEP, with subsequent advancements by Lee. Building upon these foundations, we extend Lee’s work, presenting transition probability formulas for different initial conditions, thus expanding our knowledge of ASEP dynamics. By explaining these equations, we improve the understanding of matrix elements inside the ASEP framework, leading to deeper insights across various fields of application.