THE PROBABILITY DISTRIBUTION OF THE SPECIES-1 PARTICLE IN THE TWO-SPECIES ASEP WITH INITIAL CONFIGURATION 22...21

Abstract

In this paper, we investigate the behaviour of the unique right-most species-1 particle in the 2-species ASEP. We start with the introduction, where we first introduce the model itself, which was introduced by Frank Spitzer in the paper [4]. Then we give a brief outline of the research done in the field, and the results obtained by Sch¨utz (in the paper [3]), Tracy and Widom (in the papers [5], [6]), Lee (in the papers [1], [2]), and Raimbekov (in the paper [2]). We then proceed to the preliminary section, where we explain the necessary background needed to understand the thesis. After that, we start experimenting with some special cases of the general N-particle problem; this will naturally lead us to the main results section. The main result of the thesis is the integral formula for the probability distribution of the unique species-1 particle which is right-most at time t = 0 in a 2-species ASEP.