Critical One-dimensional Multi-particle DLA

Abstract: In multi-particle Diffusion Limited Aggregation (DLA) a sea of particles perform independent random walks until they run into the aggregate and are absorbed. In dimension 1, the rate of growth of the aggregate depends on lambda, the density of the particles. Kesten and Sidoravicius proved that when $\lambda <1$ the aggregate grows like $t^{1/2}$. They furthermore predicted linear growth when $\lambda > 1$ (subsequently confirmed) and $t^{2/3}$ growth at the critical density $\lambda =1$.

In this talk we address the critical case, confirming the $t^{2/3}$ rate of growth and show that aggregate has a scaling limit whose derivative is a self-similar diffusion process. Surprisingly this contradicts conjectures on the speed in the mildly supercritical regime when $\lambda = 1 + \epsilon$.

Joint work with Danny Nam and Dor Elboim

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .