1 citations · 2 across the 10 of their papers we have counts for
10 papers
Alexandrov spaces with non negative curvature and displacement convexity of the entropy tensor
Jordan Serres
On a smooth Riemannian manifold, Aishwarya, Rotem and Shenfeld characterised nonnegative sectional curvature as the matrix displacement convexity of an entropy tensor, the Lagrangi…
means with learned metrics
Pablo Groisman, Matthieu Jonckheere, Jordan Serres +1
We study the Fréchet means of a metric measure space when both the measure and the distance are unknown and have to be estimated. We prove a general result that states that the…
A Generalization of Caffarelli's Contraction Theorem to Nearly Spherical Manifolds
Yuxin Ge, Jordan Serres
We show that every nearly spherical manifold can be realized as the volume-preserving image of a round sphere, via the Brenier-McCann optimal transport map. This theorem extends Ca…
Finite sample bounds for barycenter estimation in geodesic spaces
Victor-Emmanuel Brunel, Jordan Serres
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support con…
A generalization of Grünbaum's inequality in RCD-spaces
Victor-Emmanuel Brunel, Shin-ichi Ohta, Jordan Serres
We generalize Grünbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to -spaces with …
Concentration of empirical barycenters in metric spaces
Victor-Emmanuel Brunel, Jordan Serres
Barycenters (aka Fréchet means) were introduced in statistics in the 1940's and popularized in the fields of shape statistics and, later, in optimal transport and matrix analysis.…
Behavior of the Poincar{é} constant along the Polchinski renormalization flow
Jordan Serres
We control the behavior of the Poincar{é} constant along the Polchinski renormalization flow using a dynamic version of -calculus. We also treat the case of higher order eigenva…
Stability of higher order eigenvalues in dimension one
Jordan Serres
We study stability of the eigenvalues of the generator of a one dimensional reversible diffusion process satisfying some natural conditions. The proof is based on Stein's method. I…
Stability estimates for the sharp spectral gap bound under a curvature-dimension condition
Max Fathi, Ivan Gentil, Jordan Serres
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative…
Stability of Poincar{é} constant
Jordan Serres
We study stability of the sharp Poincar{é} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on…