Edward Crane

Particles and Permutations

I will talk about a random aggregation process in which every integer is a site that is either vacant or occupied. Initially all large negative sites are occupied and all large positive sites are vacant. Particles jump in the positive direction along the integer line, coming from minus infinity. Each one settles in the first vacant site that it encounters, making it occupied. I will explain the motivation behind the model, what I and my collaborators have proved about it, including its close connection to the asymmetric exclusion process and to some fascinating random permutations of the integers called the Mallows permutations.

Based on joint work with Marton Balazs (Bristol), Jessica Jay (formerly at Bristol, now at Lancaster) and Debleena Thacker (Durham).