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Convergence of directed random graphs to the Poisson-weighted infinite tree
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- Gabrysch, Katja (author)
- Uppsala universitet,Analys och sannolikhetsteori
- (creator_code:org_t)
- 2016-06-21
- 2016
- English.
- In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:2, s. 463-474
- Journal article (peer-reviewed)
Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- Directed random graph
- Poisson-weighted infinite tree
- rooted geometric graph
Publication and Content Type
- ref (subject category)
- art (subject category)
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