Bernoulli

  • Bernoulli
  • Volume 25, Number 4B (2019), 3479-3495.

Two-sided infinite-bin models and analyticity for Barak–Erdős graphs

Bastien Mallein and Sanjay Ramassamy

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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 $(0,1]$.

Article information

Source
Bernoulli, Volume 25, Number 4B (2019), 3479-3495.

Dates
Received: December 2017
Revised: August 2018
First available in Project Euclid: 25 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.bj/1569398774

Digital Object Identifier
doi:10.3150/18-BEJ1097

Mathematical Reviews number (MathSciNet)
MR4010962

Zentralblatt MATH identifier
07110145

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

Citation

Mallein, Bastien; Ramassamy, Sanjay. Two-sided infinite-bin models and analyticity for Barak–Erdős graphs. Bernoulli 25 (2019), no. 4B, 3479--3495. doi:10.3150/18-BEJ1097. https://projecteuclid.org/euclid.bj/1569398774


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