106 citations · 234 across the 33 of their papers we have counts for
9 papers · 1 filter
Limit law for number of components of fixed sizes of graphs with degree one or two
Nicolas Broutin, Élie de Panafieu
We consider graphs with vertices of degree 1 or 2 and prove that the numbers of components of sizes 2 to q have a limit normal distribution for any q > 1. The result is also extend…
Scaling limits of random graph models at criticality: Universality and the basin of attraction of the Erdős-Rényi random graph
Shankar Bhamidi, Nicolas Broutin, Sanchayan Sen +1
A wide array of random graph models have been postulated to understand properties of observed networks. Typically these models have a parameter and a critical time when a…
A new encoding of coalescent processes. Applications to the additive and multiplicative cases
Nicolas Broutin, Jean-François Marckert
We revisit the discrete additive and multiplicative coalescents, starting with particles with unit mass. These cases are known to be related to some "combinatorial coalescent p…
Cutting down -trees and inhomogeneous continuum random trees
Nicolas Broutin, Minmin Wang
We study a fragmentation of the -trees of Camarri and Pitman [Elect. J. Probab., vol. 5, pp. 1--18, 2000]. We give exact correspondences between the -trees an…
Reversing the cut tree of the Brownian continuum random tree
Nicolas Broutin, Minmin Wang
Consider the Aldous--Pitman fragmentation process [Ann Probab, 26(4):1703--1726, 1998] of a Brownian continuum random tree . The associated cut tree cut$({\…
Bounded monochromatic components for random graphs
Nicolas Broutin, Ross J. Kang
We consider vertex partitions of the binomial random graph . For , we observe the following phenomenon: in any partition into asymptotically fewer than $χ(G_{…