68 citations · 75 across the 12 of their papers we have counts for
16 papers
Convex geometry of diffusion laws and gradient flows for stochastic control
Yupeng Bai, Louis-Pierre Chaintron, Zhenjie Ren +1
We study gradient-type dynamics for weak stochastic control through the laws of controlled diffusions on path space. Although the objective is generally nonconvex in the drift, a u…
A Dacorogna-Moser construction of transport maps on with application to geodesics on the space of couplings
Louis-Pierre Chaintron, Matteo Picco
A seminal work by Dacorogna and Moser introduced a way of constructing regular transport maps from a probability distribution on a bounded domain to another one. In this work, we e…
ResNets of All Shapes and Sizes: Convergence of Training Dynamics in the Large-scale Limit
Louis-Pierre Chaintron, Lénaïc Chizat, Javier Maass
We establish convergence of the training dynamics of residual neural networks (ResNets) to their joint infinite depth L, hidden width M, and embedding dimension D limit. Specifical…
Mean-field limits à la Tanaka and large deviations for particle systems with network interactions
Louis-Pierre Chaintron, Antoine Diez
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formul…
Geodesic convexity and strengthened functional inequalities in submanifolds of Wasserstein space
Louis-Pierre Chaintron, Daniel Lacker
We study the geodesic convexity of various energy and entropy functionals restricted to (non-geodesically convex) submanifolds of Wasserstein spaces with their induced geometry. We…
Propagation of weak log-concavity along generalised heat flows via Hamilton-Jacobi equations
Louis-Pierre Chaintron, Giovanni Conforti, Katharina Eichinger
A well-known consequence of the Pr{é}kopa-Leindler inequality is the preservation of logconcavity by the heat semigroup. Unfortunately, this property does not hold for more general…
Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations
Louis-Pierre Chaintron, Samuel Daudin
The purpose of this note is to provide an optimal rate of convergence in the vanishing viscosity regime for first-order Hamilton-Jacobi equations with uniformly convex Hamiltonian.…
Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations
Louis-Pierre Chaintron, Samuel Daudin
The purpose of this note is to provide an optimal rate of convergence in the vanishing viscosity regime for first-order Hamilton-Jacobi equations with purely quadratic Hamiltonian.…
Constrained non-linear estimation and links with stochastic filtering
Louis-Pierre Chaintron, Laurent Mertz, Philippe Moireau +1
This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On…
Gibbs principle with infinitely many constraints: optimality conditions and stability
Louis-Pierre Chaintron, Giovanni Conforti, Julien Reygner
We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be con…
Quasi-continuity method for mean-field diffusions: large deviations and central limit theorem
Louis-Pierre Chaintron
A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting dif…
Regularity and stability for the Gibbs conditioning principle on path space via McKean-Vlasov control
Louis-Pierre Chaintron, Giovanni Conforti
We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time,…
Existence and global Lipschitz estimates for unbounded classical solutions of a Hamilton-Jacobi equation
Louis-Pierre Chaintron
The purpose of this article is to prove existence, uniqueness and uniform gradient estimates for unbounded classical solutions of a Hamilton-Jacobi-Bellman equation. Such an equati…
Mortensen Observer for a class of variational inequalities -Lost equivalence with stochastic filtering approaches
L. P. Chaintron, Álvaro Mateos González, Laurent Mertz +1
We address the problem of deterministic sequential estimation for a nonsmooth dynamics in R governed by a variational inequality, as illustrated by the Skorokhod problem with a ref…
Propagation of chaos: a review of models, methods and applications. I. Models and methods
Louis-Pierre Chaintron, Antoine Diez
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied ma…
Propagation of chaos: a review of models, methods and applications. II. Applications
Louis-Pierre Chaintron, Antoine Diez
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied ma…