Convergence of directed random graphs to the Poisson-weighted infinite tree

• We consider a directed graph on the integers with a directed edge from vertex i to j present with probability n-1, whenever i-1(j - i). We show that the closure of vertex 0 in such a weighted random graph converges in distribution to the Poisson-weighted infinite tree as n→∞. In addition, we derive limit theorems for the length of the longest path in the subgraph of the Poisson-weighted infinite tree which has all vertices at weighted distance of at most ρ from the root.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

Directed random graph

Poisson-weighted infinite tree

rooted geometric graph

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