arXiv:1003.3852v1 [math.PR] 19 Mar 2010 Page 1 arXiv:1003.3852v1 [math.PR] 19 Mar 2010
TRANSPORT INEQUALITIES. A SURVEY NATHAEL GOZLAN, CHRISTIAN LÉONARD …

Particle-based variational inference methods (ParVIs) such as Stein variational gradient
descent (SVGD) update the particles based on the kernelized Wasserstein gradient flow for …

Abstract Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can
be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the …

We consider non-negative solutions of the fast diffusion equation ut= Δ um with m∈(0, 1) in
the Euclidean space\mathbb R^ d, d≧ 3, and study the asymptotic behavior of a natural …

The aim of this paper is to give a characterization of the dimension free concentration of
measure phenomenon in terms of transportation-cost inequalities. We apply this theorem to …

We develop the optimal transportation approach to modified log-Sobolev inequalities and to
isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some …

This paper is devoted to the study of probability measures with heavy tails. Using the
Lyapunov function approach we prove that such measures satisfy different kind of functional …

We initiate a systematic study of intrinsic dimensional versions of classical functional
inequalities which capture refined properties of the underlying objects. We focus on model …

In this paper, we consider Poincaré inequalities for non-Euclidean metrics on Rd. These
inequalities enable us to derive precise dimension free concentration inequalities for …

We consider the optimization of a smooth and strongly convex objective using constant step-
size stochastic gradient descent (SGD) and study its properties through the prism of Markov …