Critical One-dimensional Multi-particle DLA
In multi-particle Diffusion Limited Aggregation (DLA) a sea of particles performs independent random walks until they run into the aggregate and are absorbed. In dimension 1, the rate of growth of the aggregate depends on λ, the density of the particles. Kesten and Sidoravicius proved that when λ<1 the aggregate grows like t1/2. They furthermore predicted linear growth when λ>1 (subsequently confirmed by Sly) and t2/3 growth at the critical density λ=1. We address the critical case, confirming the t2/3 growth and show that aggregate has a scaling limit whose derivative is a self-similar diffusion. Surprisingly, this contradicts conjectures on the speed in the mildly supercritical regime when λ = 1 + ε.
Email Jim Nolen (firstname.lastname@example.org) for the zoom link.