5 papers · 1 filter
Multitype Lévy trees as scaling limits of multitype Bienaymé-Galton-Watson trees
Osvaldo Angtuncio Hernández, David Clancy
We establish sufficient mild conditions for a sequence of multitype Bienaymé-Galton-Watson trees, conditioned in some sense to be large, to converge to a limiting compact metric s…
Fluctuations of the giant of Poisson random graphs
David Clancy
Enriquez, Faraud, and Lemaire (2023) have established process-level fluctuations for the giant of the dynamic ErdÅs-Rényi random graph above criticality and show that the limit i…
A central limit theorem for the giant in a stochastic block model
David Clancy
We provide a simple proof for of the central limit theorem for the number of vertices in the giant for super-critical stochastic block model using the breadth-first walk of Konarov…
Near-critical bipartite configuration models and their associated intersection graphs
David Clancy
Recently, van der Hofstad, Komjáthy, and Vadon (2022) identified the critical point for the emergence of a giant connected component for the bipartite configuration model (BCM) an…
Component sizes of rank-2 multiplicative random graphs
David Clancy
We show that in three different critical regimes, the masses of the connected components of rank-2 multiplicative random graph converge to lengths of excursions of a thinned Lévy…