27 citations · 43 across the 16 of their papers we have counts for
16 papers · 1 filter
Long-time propagation of chaos and exit times for metastable mean-field particle systems
Pierre Monmarché
Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase trans…
Recent advances in the long-time analysis of killed degenerate processes and their particle approximation
Bertrand Cloez, Lucas Journel, Pierre Monmarché +2
We review some recent results of quantitative long-time convergence for the law of a killed Markov process conditioned to survival toward a quasi-stationary distribution, and on th…
An entropic approach for Hamiltonian Monte Carlo: the idealized case
Pierre Monmarché
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian…
Uniform convergence of the Fleming-Viot process in a hard killing metastable case
Lucas Journel, Pierre Monmarché
We study the long-time convergence of a Fleming-Viot process, in the case where the underlying process is a metastable diffusion killed when it reaches some level set. Through a co…
Reducing exit-times of diffusions with repulsive interactions
Paul-Eric Chaudru de Raynal, Manh Hong Duong, Pierre Monmarché +2
In this work we prove a Kramers' type law for the low-temperature behavior of the exit-times from a metastable state for a class of self-interacting nonlinear diffusion processes.…
Overdamped limit at stationarity for non-equilibrium Langevin diffusions
Pierre Monmarché, Mouad Ramil
In this note, we establish that the stationary distribution of a possibly non-equilibrium Langevin diffusion converges, as the damping parameter goes to infinity (or equivalently i…
Convergence of the kinetic annealing for general potentials
Lucas Journel, Pierre Monmarché
The convergence of the kinetic Langevin simulated annealing is proven under mild assumptions on the potential for slow logarithmic cooling schedules. Moreover, non-convergence…
Metastability for systems of interacting neurons
Eva Löcherbach, Pierre Monmarché
We study a stochastic system of interacting neurons and its metastable properties. The system consists of neurons, each spiking randomly with rate depending on its membrane pot…
Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: uniform estimates in a compact soft case
Lucas Journel, Pierre Monmarché
We establish the convergences (with respect to the simulation time ; the number of particles ; the timestep ) of a Moran/Fleming-Viot type particle scheme toward the quasi…
Simulated Annealing In With Slowly Growing Potentials
Nicolas Fournier, Pierre Monmarché, Camille Tardif
We use a localization procedure to weaken the growth assumptions of Royer [8], Miclo [4] and Zitt [9] concerning the continuous-time simulated annealing in . We show…
Elementary coupling approach for non-linear perturbation of Markov processes with mean-field jump mechanims and related problems
Pierre Monmarché
Mean-field integro-differential equations are studied in an abstract framework, through couplings of the corresponding stochastic processes. In the perturbative regime, the equatio…
Weakly self-interacting velocity jump processes for bacterial chemotaxis and adaptive algorithms
Pierre Monmarché
A self-interacting velocity jump process is introduced, which behaves in large time similarly to the corresponding self-interacting diffusion, namely the evolution of its normalize…
Ergodicity and propagation of chaos for mean field kinetic particles
Pierre Monmarché
The trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation in the presence of a convex external potential, without…
Piecewise deterministic simulated annealing
Pierre Monmarché
Given an energy potential on the Euclidian space, a piecewise deterministic Markov process is designed to sample the corresponding Gibbs measure. In dimension one an Eyring-Kramers…
On and entropic convergence for contractive PDMP
Pierre Monmarché
Explicit rate of convergence in variance (or more general entropies) is obtained for a class of Piecewise Deterministic Markov Processes such as the TCP process, relying on functio…
Hypocoercive relaxation to equilibrium for some kinetic models via a third order differential inequality
Pierre Monmarché
This paper deals with the study of some particular kinetic models, where the randomness acts only on the velocity variable level. Usually, the Markovian generator cannot satisfy an…