Averaging principle and shape theorem for growth with memory.

Seminar: Probability Seminar | November 7 | 3-4 p.m. | 1011 Evans Hall

 Amir Dembo, Stanford University

 Department of Statistics

We consider a family of random growth models in n-dimensional space. These models capture certain features expected to manifest at the mesoscopic level for certain self-interacting microscopic dynamics (such as once-reinforced random walk with strong reinforcement and origin-excited random walk). In a joint work with Pablo Groisman, Ruojun Huang and Vladas Sidoravicius, we establish for such models an averaging principle and deduce from it the convergence of the normalized domain boundary, to a limiting shape. The latter is expressed in terms of the invariant measure of an associated Markov chain.