Fluctuations and mixing for Internal DLA on cylinders

Silvestri Vittoria, University of Rome La Sapienza

Internal DLA models the growth of a random subset of Z^d by subsequent aggregation of particles. At each step, a new particle starts inside the current aggregate, and it performs a simple random walk until reaching an unoccupied site, where it settles. The large scale properties of IDLA clusters are by now well understood. In this talk I will instead focus on Internal DLA seen as a Markov chain on the space of particle configurations on cylinder graphs. I will present a coupling technique for bounding the maximal fluctuations of IDLA clusters, which allows us to show that the stationary distribution concentrates on a small subset of the infinite state space. I will then discuss the mixing time of the chain, and its dependence on the choice of the cylinder’s base graph. Based on joint work with Lionel Levine (Cornell University).

Area: IS18 - Mixing times (Federico Sau)

Keywords: Random growth models

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