Abstract
In this article, we prove that for any probability distribution $\mu $ on $\mathbb{N}$ 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 $\mu $. 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–Erdős graph of parameter $p$ is analytic on $(0,1]$.
Citation
Bastien Mallein. Sanjay Ramassamy. "Two-sided infinite-bin models and analyticity for Barak–Erdős graphs." Bernoulli 25 (4B) 3479 - 3495, November 2019. https://doi.org/10.3150/18-BEJ1097
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