# Mathematics Colloquia and Seminars

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### Polynuclear growth model and random matrix with an external source

**Mathematical Physics & Probability**

Speaker: | Dr. Takashi Imamura, University of Tokyo, Department of Physics |

Location: | 593 Kerr |

Start time: | Tue, Mar 15 2005, 3:10PM |

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.