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In 1986 Kardar, Parisi, and Zhang
proposed a stochastic PDE for the motion of driven interfaces,
in particular for growth processes with local updating rules. The solution to
the 1D KPZ equation
can be approximated through the weakly asymmetric simple exclusion process.
Based on work of
Tracy and Widom on the PASEP, we obtain an exact formula for the one-point
generating function of the KPZ
equation in case of sharp wedge initial data. Our result is valid for all
times, but of particular interest is
the long time behavior, related to random matrices, and the finite time
corrections. This is joint work with
Tomohiro Sasamoto. |
