Session S06 - Interacting Stochastic Systems

Wednesday, July 14, 14:50 ~ 15:25 UTC-3

Scaling limit for heavy-tailed ballistic deposition with $p$-sticking

Santiago Saglietti

Pontificia Universidad Católica, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Ballistic deposition is a model for interface growth in which unit blocks fall vertically at random over the different sites of $\mathbb{Z}$ and stick to the interface at the first point of contact, causing it to grow. We consider a variant of this model in which the blocks have random heights, which are i.i.d. with some common distribution having a heavy right tail, and each block can only stick to the interface at the first point of contact with probability $p$ (otherwise, it continues to fall vertically until it lands on some previously deposited block). We study scaling limits of the resulting interface for the different values of $p$ and show that there is a phase transition as $p$ goes from $1$ to $0$.

Joint work with Francis Comets (Université de Paris, France) and Joseba Dalmau (NYU-Shanghai, China).

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