Open Access
November 2019 Two-sided infinite-bin models and analyticity for Barak–Erdős graphs
Bastien Mallein, Sanjay Ramassamy
Bernoulli 25(4B): 3479-3495 (November 2019). DOI: 10.3150/18-BEJ1097


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 $(0,1]$.


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Bastien Mallein. Sanjay Ramassamy. "Two-sided infinite-bin models and analyticity for Barak–Erdős graphs." Bernoulli 25 (4B) 3479 - 3495, November 2019.


Received: 1 December 2017; Revised: 1 August 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110145
MathSciNet: MR4010962
Digital Object Identifier: 10.3150/18-BEJ1097

Keywords: Barak–Erdős graphs , infinite-bin model , interacting particle systems , longest path , Random graphs , two-sided Markov chains

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4B • November 2019
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