On the length of the shortest path in a sparse Barak–Erdős graph

Bastien Mallein, Pavel Tesemnikov

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

We consider an inhomogeneous version of the Barak–Erdős graph, i.e. a directed Erdős–Rényi random graph on {1,…,n} with no loop. Given f a Riemann-integrable non-negative function on [0,1]2 and γ>0, we define G(n,f,γ) as the random graph with vertex set {1,…,n} such that for each i<j the directed edge (i,j) is present with probability pi,j(n)=[Formula presented], independently of any other edge. We denote by Ln the length of the shortest path between vertices 1 and n, and take interest in the asymptotic behaviour of Ln as n→∞.

Язык оригиналаанглийский
Номер статьи109634
ЖурналStatistics and Probability Letters
Том190
DOI
СостояниеОпубликовано - нояб. 2022

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