Limiting Properties of Random Graph Models with Vertex and Edge Weights

Sergey Foss, Takis Konstantopoulos

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on edges and vertices and assuming that weights on edges are signed. We aim at an exposition that summarizes, simplifies, and extends proof ideas. We also study sparse graph asymptotics, showing convergence of the weighted random graphs to a certain weighted graph that can be constructed in terms of Poisson processes. We are motivated by numerous applications, ranging from ecology to parallel computing models. It is the latter set of applications that necessitates the introduction of vertex weights. Finally, we discuss some open problems and research directions.

Язык оригиналаанглийский
Страницы (с-по)626-643
Число страниц18
ЖурналJournal of Statistical Physics
Том173
Номер выпуска3-4
DOI
СостояниеОпубликовано - 1 ноя 2018

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