A dynamical approach to spanning and surplus edges of random graphs

Abstract

Consider a finite inhomogeneous random graph running in continuous time, where each vertex has a mass, and the edge that links any pair of vertices appears with a rate equal to the product of their masses. The simultaneous breadth-first-walk introduced by Limic (2019) is extended in order to account for the surplus edge data in addition to the spanning edge data. Two different graph-based representations of the multiplicative coalescent, with different advantages and drawbacks, are discussed in detail. A canonical multi-graph from Bhamidi, Budhiraja and Wang (2014) naturally emerges. The presented framework will facilitate the understanding of scaling limits with surplus edges for near-critical random graphs in the domain of attraction of general (not necessarily standard) eternal augmented multiplicative coalescent.

Josué Corujo Rodríguez
Josué Corujo Rodríguez
Maître de Conférences

My research interests is focussed in probability theory, specifically stochastic processes and their applications.

Vlada Limic
Directrice de Recherche CNRS