Fisher Information in Kinetic Theory
Abstract
These notes review the theory of Fisher information, especially its use in kinetic theory of gases and plasmas. The recent monotonicity theorem by Guillen--Silvestre for the Landau--Coulomb equation is put in perspective and generalised. Following my joint work with Imbert and Silvestre, it is proven that Fisher information is decaying along the spatially homogeneous Boltzmann equation, for all relevant interactions, and from this the once longstanding problem of regularity estimates for very singular collision kernels (very soft potentials) is solved.
Keywords
Cite
@article{arxiv.2501.00925,
title = {Fisher Information in Kinetic Theory},
author = {Cédric Villani},
journal= {arXiv preprint arXiv:2501.00925},
year = {2025}
}
Comments
Lecture Notes from a course at the Mathemata Summer School at Festum Pi, Chania (Crete), July 2024. V2 corrected and augmented after a careful referee report. V3: Remark 8.11 added. V4, V5: Minor corrections