A universality property of the one-sided ballistic deposition model near the time axis

par Alejandro Ramirez

jeudi 4 déc. 2025, 14:00 → 15:00 Europe/Paris

112 (ICJ)

Ballistic deposition is a model of interface growth introduced by Vold in 1959 which has remained largely mathematically intractable. In dimension d=2, it is conjectured to belong to the KPZ universality class. It is defined as a process of vertically falling blocks that stick to the top, the right or the left of growing columns. Here we introduce a variant, the one sided ballistic deposition model, in which vertically falling blocks can only stick to the top or the upper right corner of growing columns. We establish that in dimension d=2, strong KPZ universality holds near the time axis, proving that the fluctuations of the height function there are given by the Tracy-Widom GUE distribution. The proof is based on a graphical construction of the process in terms of a last passage percolation model.

This talk is based on a joint work with Pablo Groisman, Santiago Saglietti and Sebastián Zaninovich.