Journée de l’équipe ALEA-PROBA

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Date(s) - 06/12/2019
10 h 00 min - 17 h 45 min

FRUMAM, St Charles (3ème étage)



10h-10h45 – Mathieu GÉNOIS
Titre: Analysis of complex networks using randomized reference models

11h-11h45 – Raphael FORIEN
Titre : Household epidemic models and McKean-Vlasov Poisson driven SDEs

In this talk I will present an epidemic model where susceptible and infected individuals are distributed in discrete households of finite size. Infected individuals can either infect other individuals in the same household or individuals chosen uniformly in the whole population. When the number of households tends to infinity, we obtain a limit for the epidemic process given in terms of a nonlinear Markov process which solves a McKean-Vlasov Poisson driven SDE. We also prove a propagation of chaos result. Finally, we define a basic reproduction number R0, and show that if R0>1, then the nonlinear Markov process has a unique non trivial ergodic invariant probability measure (i.e. the epidemic spreads to a large proportion of the population with positive probability), whereas if R0<=1, the non-linear Markov process converges to 0 as t tends to infinity (the epidemic quickly dies out).

This is joint work with Étienne Pardoux.

14h30-15h15 – Sacha BUFETOV
Titre: Entire functions corresponding to determinant point processes (résumé ci-après en pdf)


15h30-16h15 – Amine ASSELAH
Titre: Moderate Deviation for the volume of the range of a transient random
We obtain moderate deviation estimates for the volume of the range for a transient random walk on the euclidean lattice. Joint work with Bruno S.

17h-17h45 – Pierre PICCO
Titre : Le phénomène de la separation des phases pour le modèle d’Ising unidimensionnel avec interaction à longues portées

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