THE PROBABILITY DISTRIBUTION OF THE SPECIES-1 PARTICLE IN THE TWO-SPECIES ASEP WITH INITIAL CONFIGURATION 22...21
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Date
2022-04
Authors
Tokebayev, Zhanibek
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Sciences and Humanities
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.
Description
Keywords
Type of access: Open Access, ASEP
Citation
Zhanibek Tokebayev (2022). The probability distribution of the species-1 particle in the two-species ASEP with initial configuration 22...21. Nazarbayev University, Nur-sultan, Kazakhstan