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    Transition between Airy1 and Airy2 processes and TASEP fluctuations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Borodin, Alexei; Ferrari, Patrik; Sasamoto, Tomohiro
    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. F or 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 interpolati on between GOE and GUE edge distributions.