21 citations · 22 across the 5 of their papers we have counts for
6 papers
Local stability and rates of convergence to equilibrium for the Nonlinear Renewal Equation; applications to Hawkes processes
Céline Duval, Eric Luçon
We study the asymptotic properties of the solutions of a nonlinear renewal equation. The main contribution of the present article is to provide stability and convergence results ar…
Neural Field Equations and Hawkes processes: long-term stability of traveling wave profiles in the neutral case
Eric Luçon, Christophe Poquet
We consider the long-time behavior of a population of interacting Hawkes processes on the real line, with spatial extension. The large population behavior of the system is governed…
Periodicity and longtime diffusion for mean field systems in
Eric Luçon, Christophe Poquet
We study in this paper the longtime behavior of some large but finite populations of interacting stochastic differential equations whose (infinite population) limit Fokker-Planck P…
Quenched asymptotics for interacting diffusions on inhomogeneous random graphs
Eric Luçon
The aim of the paper is to address the behavior in large population of diffusions interacting on a random, possibly diluted and inhomogeneous graph. This is the natural continuatio…
Long time dynamics and disorder-induced traveling waves in the stochastic Kuramoto model
Eric Luçon, Christophe Poquet
The aim of the paper is to address the long time behavior of the Kuramoto model of mean-field coupled phase rotators, subject to white noise and quenched frequencies. We analyse th…
Quenched limits and fluctuations of the empirical measure for plane rotators in random media
Eric Luçon
The Kuramoto model has been introduced to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. The model consists of interacting oscillat…