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Transition between Airy 1 and Airy 2 processes and TASEP fluctuations
Author(s) -
Borodin Alexei,
Ferrari Patrik L.,
Sasamoto Tomohiro
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20234
Subject(s) - asymmetric simple exclusion process , mathematics , universality (dynamical systems) , airy function , statistical physics , random matrix , particle system , stochastic matrix , mathematical analysis , physics , quantum mechanics , markov chain , eigenvalues and eigenvectors , statistics , computer science , operating system
We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions, starting with certain deterministic initial conditions. For large time t , one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy 1 and Airy 2 processes, whose one‐point distributions are the GOE and GUE Tracy‐Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one‐point distribution is a new interpolation between GOE and GUE edge distributions. © 2007 Wiley Periodicals, Inc.