Date/heure
20 octobre 2022
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Josué Corujo (Université de Strasbourg)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
During this talk, we will review some recent advances in the multiplicative coalescent theory and its link to random graphs. The multiplicative coalescent dynamic naturally emerges when one regards the evolution of the connected components in a graph-valued Markov process. We will mainly focus on the breadth-first walk introduced by V. Limic (2019), a Lévy-type process encoding a random forest whose components (trees) are a representation of the multiplicative coalescent. We will then focus on the extension of this construction to account for the surplus edges data, in addition to the spanning edge data. We will present two different graph representations of the multiplicative coalescent, with different advantages and drawbacks, that are discussed in detail. In particular, we will show how to recover a realization of the random graph at a fixed time, and also as a process when the time parameter evolves. We will also discuss the use of these results to understand the scaling limits of near-critical random graphs in the domain of attraction of general eternal multiplicative coalescent.