Symmetric diffusions with polynomial eigenvectors

Dominique Bakry (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension, some basic examples arise from compact Lie groups. We give a complete description of the bounded sets on which such operators may live. We then provide a classification of those sets when the polynomials are ordered according to their usual degrees

Mots clés: orthogonal polynomials; diffusion operators; random matrices

Domaines: Probabilités [math.PR]

Dominique Bakry. Symmetric diffusions with polynomial eigenvectors. Crisan D., Hambly B., Zariphopoulou T. (eds). Stochastic Analysis and Applications, 2014, Springer Proceedings in Mathematics & Statistics, vol. 100, 978-3-319-11291-6. ⟨10.1007/978-3-319-11292-3_2⟩. ⟨hal-00966942⟩