Curvature dimension bounds on the deltoid model

Dominique Bakry (1) , Olfa Zribi (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

The deltoid curve in R 2 is the boundary of a domain on which there exist probability measures and orthogonal polynomials for theses measures which are eigenvec-tors of diffusion operators. As such, they may be considered as a two dimensional extension of the classical Jacobi operators. They belong to one of the 11 families of such bounded domains in R 2. We study the curvature-dimension inequalities associated to these operators, and deduce various bounds on the associated polynomials, together with Sobolev inequalities related to the associated Dirichlet forms

Domaines: Probabilités [math.PR]

Dominique Bakry, Olfa Zribi. Curvature dimension bounds on the deltoid model. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2016, vol. 25 (1), pp.65-90. ⟨10.5802/afst.1487⟩. ⟨hal-01135079⟩