# Alexandre Stauffer

University of Bath

### Multi-particle diffusion limited aggregation

Probability Seminar
11th May 2018, 3:30 pm – 4:30 pm
Main Maths Building, SM2

We consider a random model for the growth of an aggregate on Z^d, motivated by processes from physics such as dielectric breakdown and electrodeposition. Start with an infinite collection of particles located at the vertices of the lattice, with at most one particle per vertex, and initially distributed according to the product Bernoulli measure with parameter $\mu\in(0,1)$. In addition, there is an aggregate, which initially consists of only one particle placed at the origin. Non-aggregated particles move as continuous time simple symmetric random walks obeying the exclusion rule, whereas aggregated particles do not move. The aggregate grows indefinitely by attaching particles to its surface whenever a particle attempts to jump onto it. In the talk I will survey the known results about this model, and talk about our result on the speed of growth of the aggregate.

This is a joint work with Vladas Sidoravicius.

Organisers: Tyler Helmuth, Ofer Busani