4 papers
Isoperimetric and geometric inequalities in quantitative form: Stein's method approach
Jordan Serres
We adapt Stein's method to isoperimetric and geometric inequalities. The main challenge is the treatment of boundary terms. We address this by using an elliptic PDE with an oblique…
Generalized perimeters and gradient estimates
Jordan Serres
We use a variational formulation to define a generalized notion of perimeter, from which we derive abstract isoperimetric Cheeger's inequalities via gradient estimates on solutions…
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…