Asymptotic distribution of entry times in a cellular automaton with annihilating particles
Petr Kůrka (1), Enrico Formenti (2), Alberto Dennunzio (3) (2)
(1) Center for Theoretical Study [Prague]
(2) Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
(3) Dipartimento di Informatica Sistemistica e Comunicazione
Abstract
This work considers a cellular automaton (CA) with two particles: a stationary particle $1$ and left-going one $\overline{1}$. When a $\overline{1}$ encounters a $1$, both particles annihilate. We derive asymptotic distribution of appearence of particles at a given site when the CA is initialized with the Bernoulli measure with the probabilities of both particles equal to $1/2$.
