Height Distributions of 1D KPZ Equation with Sharp Wedge Initial Conditions.
Wed, September 22, 2010 2:00PM - 3:00PM
| Time: | 2:00PM - 3:00PM |
| Location: | Simons Auditorium |
| Speakers: | Tomohiro Sasamoto, Tomohiro Sasamoto |
| Abstract: | The Kardar-Parisi-Zhang (KPZ) equation is a nonlinear stochastic
differential equation which describes surface growth.
We consider the one-dimensional version of the equation with
sharp wedge initial conditions. We show that the distributions
of the height is written as an integral of a Fredholm determinant.
We discuss a few properties of the solution. In the long time
limit it tends to the GUE Tracy-Widom distribution. The first order
correction is of t^{-1/3} which is consistent with a recent
experiment of liquid crystal turbulence. We also explain the
derivation of our results based on the contour integral formula for
ASEP by Tracy and Widom.
This is based on a collaboration with H. Spohn. |
