Stability of higher order eigenvalues in dimension one

Jordan Serres (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study stability of the eigenvalues of the generator of a one dimensional reversible diffusion process satisfying some natural conditions. The proof is based on Stein's method. In particular, these results are applied to the Normal distribution (via the Ornstein-Uhlenbeck process), to Gamma distributions (via the Laguerre process) and to Beta distributions (via Jacobi process).

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Probabilités [math.PR]; Théorie spectrale [math.SP]

Jordan Serres. Stability of higher order eigenvalues in dimension one. 2022. ⟨hal-03681812⟩