### Abstract of "Transition between Airy_{1} and Airy_{2} processes and TASEP fluctuations"

with Alexei Borodin and Tomohiro Sasamoto.

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.

Postscript file: [PS]

PDF file: [PDF]

arXiv: math-ph/0703023