[STAT/AP] Reka Szabo: Stability results via Toom contours

18 maart 2024 15:45 t/m 16:45 - Locatie: Lecture Hall Boole | Zet in mijn agenda

In this talk I will review Toom's classical result about stability of trajectories of cellular automata. Informally, we say that a cellular automaton is stable if it does not completely lose memory of its initial state when subjected to noise. Using a contour argument Toom gave necessary and sufficient conditions for the cellular automaton to be stable. I will introduce an alternative definition of Toom contours that allows us to extend his method to more general models. I will show how this method can be used to obtain bounds for the critical parameters for certain models, as well as discuss possible applications and limitations of this extension. (Based on joint work with Jan Swart and Cristina Toninelli.)