Tokebayev, Zhanibek2022-06-212022-06-212022-04Zhanibek Tokebayev (2022). The probability distribution of the species-1 particle in the two-species ASEP with initial configuration 22...21. Nazarbayev University, Nur-sultan, Kazakhstanhttp://nur.nu.edu.kz/handle/123456789/6288In 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.enAttribution-NonCommercial-ShareAlike 3.0 United StatesType of access: Open AccessASEPMaster's thesis