Transparencies in Postscript and in PDF.

We will introduce basic shape theory for random monotone local rules, and will discuss proofs for the existence of such shapes as well as their characterization through the Wulff construction.

Transparencies in Postscript and in PDF.

This talk will discuss properties of growth models when the updates are nearly deterministic. Sometimes such random dynamics retain their deterministic shapes. We will characterize such cases in two dimensions.

Transparencies in Postscript and in PDF.

Two discrete growth models with an update probability p will be discussed. One is exactly solvable in the limit as p goes to 0, the other for every p. The exact solution allows one to compute the shape explicitly and to determine the fluctutations around it.

Transparencies in Postscript and in PDF.

Bootstrap percolation is a well known model for rare nucleation. We will review its properties, focusing on its behavior in an environment of inert obstacles.