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arXiv · 2607.13814

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

Paul Alphonse·Jean-Marc Bouclet·Matthieu Léautaud
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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.

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Paul Alphonse, Jean-Marc Bouclet, Matthieu Léautaud. 2026-07-15. Short-time parametrix for the Fokker--Planck semigroup and applications. https://arxiv.org/abs/2607.13814

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