Pith. sign in

REVIEW 8 cited by

Fisher Information in Kinetic Theory

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2501.00925 v5 pith:U2TKMFQV submitted 2025-01-01 math.AP math-phmath.MP

Cédric Villani This is my paper · ORCID
classification math.APmath-phmath.MP
keywords fisherinformationtheoryequationkineticveryalongboltzmann
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Kac's Program for the Landau Equation

    math.AP 2025-06 conditional novelty 8.0 of 10

    The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L...

  2. The Homogeneous Landau Equation with Regularised Thermal Noise

    math.AP 2026-07 conditional novelty 7.0 of 10

    Weak solutions exist for a regularised fluctuating homogeneous Landau equation with moderately soft potentials, small conservative noise in Landau-divergence form, and a refined entropy decay when the noise modes are ...

  3. Quantitative propagation of chaos for the Boltzmann equation with moderately soft potentials

    math.AP 2026-07 accept novelty 7.0 of 10

    For moderately soft potentials (-1<γ<0), the Kac particle empirical measure converges to the Boltzmann solution with quantitative W2 rate N^{-1/3}+N^{-ℓ(q,γ)}; first such rate.

  4. Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms

    math.ST 2026-07 conditional novelty 6.0 of 10

    Same-sample stabilized HOIF estimators for bilinear forms are √n-CAN for k=o(n) and more numerically stable than sample-split empirical HOIFs.

  5. The fuzzy Landau equation: global well-posedness and Fisher information

    math.AP 2025-07 conditional novelty 6.0 of 10

    The fuzzy Landau equation has unique global smooth solutions for moderately soft potentials, and its spatial Fisher information decreases monotonically over time.

  6. From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties

    math-ph 2025-07 conditional novelty 5.0 of 10

    The authors extend Energy Distances to negative and higher orders, connect them to Fourier-based metrics, and construct scale-invariant divergence measures for high-dimensional machine learning.

  7. On a fuzzy Landau Equation: Part II. Solvability results

    math.AP 2025-07 conditional novelty 5.0 of 10

    Global existence of entropy-dissipating H-solutions is established for the fuzzy Landau equation with power-law and very-soft kernels, together with a priori propagation estimates for moments and Lp norms.

  8. The Landau equation and Fisher information

    math.AP 2025-07 accept novelty 4.0 of 10

    The Fisher information is non-increasing along solutions of the homogeneous Landau equation with Coulomb potential, ruling out finite-time singularity formation.

Pith tools