8 papers
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 sp…
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 Erdős-Rényi random graph above criticality and show that the limit is…
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…
Asymptotics for the number of bipartite graphs with fixed surplus
David Clancy
In a recent work on the bipartite Erdős-Rényi graph, Do et al. (2023) established upper bounds on the number of connected labeled bipartite graphs with a fixed surplus. We use some…
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) and…
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 p…
Degree corrected stochastic block model: excursion representation
David Clancy, Vitalii Konarovskyi, Vlada Limic
This is the first of two complementary works in which we analyze the connected components of the degree-corrected stochastic block model (DCSBM). Our model is a random graph with a…
Inhomogeneous percolation on the hierarchical configuration model with a heavy-tailed degree distribution
David Clancy
We consider inhomogeneous percolation on a hierarchical configuration model with a heavy-tailed degree distribution. This graph is the configuration model where all the half-edges…