6 papers
How to construct decay rates for kinetic Fokker--Planck equations?
Giovanni Brigati, Gabriel Stoltz
We study time averages for the norm of solutions to kinetic Fokker--Planck equations associated with general Hamiltonians. We provide fully explicit and constructive decay estimate…
Kinetic Optimal Transport (OTIKIN) -- Part 1: Second-Order Discrepancies Between Probability Measures
Giovanni Brigati, Jan Maas, Filippo Quattrocchi
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framew…
From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
Gennaro Auricchio, Giovanni Brigati, Paolo Giudici +1
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Lei…
Explicit convergence rates of underdamped Langevin dynamics under weighted and weak Poincaré--Lions inequalities
Giovanni Brigati, Gabriel Stoltz, Andi Q. Wang +1
We study the long-time behavior of the underdamped Langevin dynamics, in the case of so-called \emph{weak confinement}. Indeed, any distribution (in position an…
Hypocoercivity meets lifts
Giovanni Brigati, Francis Lörler, Lihan Wang
We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack, with the notion of second-order lifts of reversible diffu…
Multivariate Gini-type discrepancies
Gennaro Auricchio, Giovanni Brigati, Paolo Giudici +1
Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between…