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Analyticity of the growth rate of the longest path in Barak-Erd\H{o}s graphs. (arXiv:1712.09985v1 [math.PR])
来源于:arXiv
In this article, we prove that for any probability distribution $\mu$ on
$\mathbb{N}$ one can construct a 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-Erd\H{o}s
graph of parameter $p$ is analytic on $(0,1]$. 查看全文>>