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math.AP2026
Short-time parametrix for the Fokker--Planck semigroup and applications
Paul Alphonse, Jean-Marc Bouclet, Matthieu Léautaud
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 semigr…
math.AP2026
A quantitative averaging lemma for spatially dependent vector fields
Paul Alphonse, Billel Guelmame, Julien Vovelle
We prove a quantitative averaging lemma for spatially dependent vector fields. Our proof is based on an iteration of the regularizing operator and some elementary considerations ab…
math.AP2024
A smoothing effect for the fractional Schrödinger equations on the circle and observability
Paul Alphonse, Nikolay Tzvetkov
We show that, after a renormalisation, one can define the square of the modulus of the solution of the fractional Schrödinger equations on the circle with data in Sobolev spaces of…