Nucleation of lines in two-dimensional growth models

In a nucleation process, formation of small nuclei initiates displacement of one equilibrium by another. Typically, nucleation is local: diameter of the nuclei is much smaller than the time-scale of convergence to the new state. We will discuss a few simple models in which this is not true; instead, the nuclei generate lower-dimensional structures that grow and interact significantly before most of the space is affected. Analysis of such models includes a variety of combinatorial and probabilistic methods.

The talk will be aimed at the general audience.