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Polynuclear growth model and random matrix with an external source
Probability| Speaker: | Dr. Takashi Imamura, University of Tokyo, Department of Physics |
| Location: | 593 Kerr |
| Start time: | Tue, Mar 15 2005, 3:10PM |
Description
The polynuclear growth (PNG) model is a simple
random growth model which belongs to the Kardar-Parisi-Zhang
(KPZ) universality class. Recently, it has been found that
the limiting distribution of the height fluctuation in
the PNG model is equivalent to the Tracy-Widom distribution,
which is the limiting distribution of the largest eigenvalue
in the random matrix theory (RMT).
In this talk, we discuss how the distribution of the height
fluctuation depends on an external source at an edge in
the PNG model, and then present a random matrix interpretation
of the distribution function. The random matrix ensemble
obtained here is a special case of a random matrix with an
external source. We further investigate a certain non-colliding
Brownian motion model which is closely related to the PNG model
with the external source. We show that the random matrix ensemble
is obtained naturally from a joint distribution function of the
non-colliding Brownian motion model.