2 citations · 6 across the 7 of their papers we have counts for
7 papers
A novel approach to the giant component fluctuations
Josué Corujo, Sophie Lemaire, Vlada Limic
We present a novel approach to study the evolution of the size (i.e. the number of vertices) of the giant component of a random graph process. It is based on the exploration algori…
The process of fluctuations of the giant component of an Erdős-Rényi graph
Nathanaël Enriquez, Gabriel Faraud, Sophie Lemaire
We present a detailed study of the evolution of the giant component of the Erdős-Rényi graph process as the mean degree increases from 1 to infinity. It leads to the identification…
A multiplicative coalescent with asynchronous multiple mergers
Sophie Lemaire
We define a Markov process on the partitions of by drawing a sample in at each time of a Poisson process, by merging blocks that contain one of these poi…
Markovian loop clusters on the complete graph and coagulation equations
Sophie Lemaire
Poissonian ensembles of Markov loops on a finite graph define a random graph process in which the addition of a loop can merge more than two connected components. We study Markov l…
Markovian loop clusters on graphs
Yves Le Jan, Sophie Lemaire
We study the loop clusters induced by Poissonian ensembles of Markov loops on a finite or countable graph (Markov loops can be viewed as excursions of Markov chains with a random s…
Diffusion approximation of a multilocus model with assortative mating
Alison M. Etheridge, Sophie Lemaire
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequen…