Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Limiting Properties of Random Graph Models with Vertex and Edge Weights. / Foss, Sergey; Konstantopoulos, Takis.
в: Journal of Statistical Physics, Том 173, № 3-4, 01.11.2018, стр. 626-643.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Limiting Properties of Random Graph Models with Vertex and Edge Weights
AU - Foss, Sergey
AU - Konstantopoulos, Takis
N1 - Publisher Copyright: © 2018, The Author(s).
PY - 2018/11/1
Y1 - 2018/11/1
N2 - 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.
AB - 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.
KW - Limit theorems
KW - Random graphs
KW - Stochastic networks
KW - CONVERGENCE
KW - LEVEL-SPACING DISTRIBUTIONS
UR - http://www.scopus.com/inward/record.url?scp=85049585076&partnerID=8YFLogxK
U2 - 10.1007/s10955-018-2080-3
DO - 10.1007/s10955-018-2080-3
M3 - Article
AN - SCOPUS:85049585076
VL - 173
SP - 626
EP - 643
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 3-4
ER -
ID: 14405759