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

Stability of higher order eigenvalues in dimension one