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

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 $(0,1]$.

Title changed and Section 1 rewritten. 16 pages, 1 figure

References in corpus (2)

• Branching random walk with selection at critical rate
• Coupling any number of balls in the infinite-bin model

Cited by in corpus (3)

• Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation
• Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models
• Freezing in the Infinite-Bin Model