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In 1986 Kardar, Parisi, and Zhang proposed a stochastic PDE for the motion of driven interfaces. Bertini and Giacomin (1997) explained how to approximate the solution to the 1D KPZ equation through the weakly asymmetric simple exclusion process. Based on work of Tracy and Widom on the PASEP, we report a formula for the one-point generating function of the KPZ equation in the case of sharp wedge initial data. The long time limit is given by the Tracy-Widom distribution from GUE random matrices. Of particular interest are the finite time corrections. This is joint work with Tomohiro Sasamoto.

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Herbert Spohn, Technische Universität München
Seminarraum Theoretische Physik
Contact: not specified