Short-time parametrix for the Fokker--Planck semigroup and applications

Paul Alphonse; Jean-Marc Bouclet; Matthieu Léautaud

Short-time parametrix for the Fokker--Planck semigroup and applications

Analysis of PDEs 2026-07-15 v1

Authors: Paul Alphonse , Jean-Marc Bouclet , Matthieu Léautaud

Abstract

We construct a short-time parametrix for the Fokker--Planck semigroup in Euclidean space. Among possible applications, we obtain smoothing and localization properties of the semigroup, the derivation of an approximate short-time polar decomposition for the semigroup, the construction of a parametrix of the resolvent, pseudospectral estimates, and estimates of the asymptotics of the number of eigenvalues of the Fokker--Planck operator. As a step in the proofs, we introduce a class of operators, which we call subsectorial operators, to which the Fokker--Planck operator belongs, and describe some of their functional analytic and spectral properties.

Keywords

Fokker-Planck semigroup short-time parametrix polar decomposition pseudospectral estimates subsectorial operators eigenvalue asymptotics

Cite

@article{arxiv.2607.13814,
  title  = {Short-time parametrix for the Fokker--Planck semigroup and applications},
  author = {Paul Alphonse and Jean-Marc Bouclet and Matthieu Léautaud},
  journal= {arXiv preprint arXiv:2607.13814},
  year   = {2026}
}