Averaging principle and random growth – Ruojun Huang (Scuola Normale Superiore)

Abstract

Motivated by questions in reinforced random walks and the asymptotic shape of their range, we study a simplified model of random growth in the continuum. In this model, random sets grow by increment of small bumps at the boundary, driven by a particle that is confined to move in its interior, reinforced by the last location of domain’s increment. We prove scaling limit of the growing domain to an infinite dimensional ODE, when the bump size is sent to zero. We deduce a macroscopic shape theorem for the growing domain with fixed bump size, as time tends to infinity. Joint work with Amir Dembo, Pablo Groisman, and Vladas Sidoravicius.

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