Transition between Airy_1 and Airy_2 processes and TASEP fluctuations

Details Transition between Airy_1 and Airy_2 processes and TASEP fluctuations Transition between Airy_1 and Airy_2 processes and TASEP fluctuations

2007-03-07

arxiv.org/abs/math-ph/0703023v1

Comm. Pure Appl. Math. 61 (2008), 1603-1629

Physics

Mathematical Physics

28 pages, 5 figures, LaTeX

Scientific paper

10.1002/cpa.20234

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.

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