English

Curvature dimension bounds on the deltoid model

Probability 2015-03-25 v1

Abstract

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

Keywords

Cite

@article{arxiv.1503.07123,
  title  = {Curvature dimension bounds on the deltoid model},
  author = {Dominique Bakry and Olfa Zribi},
  journal= {arXiv preprint arXiv:1503.07123},
  year   = {2015}
}