Two-sided infinite-bin models and analyticity for Barak-Erdös graphs

Bastien Mallein (1) , Sanjay Ramassamy (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

In this article, we prove that for any probability distribution µ on N one can construct a two-sided stationary version of the infinite-bin model –an interacting particle system introduced by Foss and Konstantopoulos– with move distribution µ. Using this result, we obtain a new formula for the speed of the front of infinite-bin models, as a series of positive terms. This implies that the growth rate C(p) of the longest path in a Barak-Erdös graph of parameter p is analytic on (0,1].

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Bastien Mallein, Sanjay Ramassamy. Two-sided infinite-bin models and analyticity for Barak-Erdös graphs. Bernoulli, 2019, 25 (4B), pp.3479-3495. ⟨10.3150/18-BEJ1097⟩. ⟨hal-01689651v2⟩