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In this article, we prove that for any probability distribution $\mu$ on$\mathbb{N}$ one can construct a two-sided stationary version of theinfinite-bin model (an interacting particle system introduced by Foss andKonstantopoulos) with move distribution $\mu$. Using this result, we obtain anew formula for the speed of the front of infinite-bin models, as a series ofpositive terms. This implies that the growth rate $C(p)$ of the longest path ina Barak-Erd\H{o}s graph of parameter $p$ is analytic on $(0,1]$.

Two-sided infinite-bin models and analyticity for Barak-Erd\H{o}s graphs