Convergence Of Directed Random Graphs To The Poisson-Weighted Infinite Tree
2016 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 53, no 2, 463-474 p.Article in journal (Refereed) PublishedText
We consider a directed graph on the integers with a directed edge from vertex i to j present with probability n(-1), whenever i < j, independently of all other edges. Moreover, to each edge (i, j) we assign weight n(-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 -> infinity. 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 rho from the root.
Place, publisher, year, edition, pages
2016. Vol. 53, no 2, 463-474 p.
Directed random graph, Poisson-weighted infinite tree, rooted geometric graph
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:uu:diva-299908DOI: 10.1017/jpr.2016.13ISI: 000378598700012OAI: oai:DiVA.org:uu-299908DiVA: diva2:950354