Department Colloquium

Department of Mathematics
Princeton University



October 11th, 2000


Limiting fluctuations in random growth models

It has been believed by physics community that for a general class of two dimensional random growth models (e.g., crystal), the limiting shape fluctuation has order (mean)^{1/3}, which should be contrasted to the linear statistics where fluctuation has order (mean)^{1/2} by the central limit theorem. In recent years, several people found a few examples of random growth models for which the above conjecture on the fluctuation can be proved. Indeed, one can also compute the distribution functions for the limiting fluctuation, which turn out to be identical to the distribution functions appeared in random matrix theory.

In this talk, we will discuss these results through the Johansson's model. We also consider an extension of Johansson's model which has a transition of the fluctuation from (mean)^{1/3} to (mean)^{1/2} as a parameter varies (joint work with E. Rains).