Diffusions with polynomial eigenvectors via finite subgroups of O(3)

Dominique Bakry (1) , Xavier Bressaud (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We provide new examples of diffusion operators in dimension 2 and 3 which have orthogonal polynomials as eigenvectors. Their construction rely on the finite subgroups of O(3) and their invariant polynomials.

Mots clés: regular polyhedra; 42C05; 47D07; diffusion operators; 33C590; 58J65; Orthogonal polynomials; diffusion processes; invariant polynomials MSC classification: 13A50

Domaines: Probabilités [math.PR]; Algèbre commutative [math.AC]; Géométrie différentielle [math.DG]

Dominique Bakry, Xavier Bressaud. Diffusions with polynomial eigenvectors via finite subgroups of O(3). Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2016, vol. 25 (2-3), pp.683-721. ⟨10.5802/afst.1508⟩. ⟨hal-01171287⟩