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.