Speaker: Inés Armendáriz - Universidad de Buenos Aires
Abstract:
The Box Ball System, or BBS for short, was introduced by Takahashi and Satsuma in 1990 as a cellular automaton that exhibits solitons (travelling waves). In a recent work, Ferrari, Nguyen, Rolla and Wang propose a hierarchical decomposition of a fixed configuration of the BBS in solitons, called the slot decomposition, and Ferrari and Gabrielli identified the distribution of this decomposition for a random walk with negative drift.In this project we extend these results to a Brownian motion with negative drift. We consider the excursions over past minima of the trajectory, and show that they can be decomposed as a superposition of solitons. These are distributed as a Poisson process in the first quadrant of the plane, with an intensity that is homogeneous in the abscissa (associated to the location of the solitons) but not in the ordinate (denoting the size of the solitons).
Joint work with Pablo Blanc, Pablo Ferrari and Davide Gabrielli