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Convergence of dire...
Convergence of directed random graphs to the Poisson-weighted infinite tree
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- Gabrysch, Katja (författare)
- Uppsala universitet,Analys och sannolikhetsteori
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(creator_code:org_t)
- 2016-06-21
- 2016
- Engelska.
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 53:2, s. 463-474
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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