Gaussian Limits and Polynomials on High Dimensional Spheres

Résumé du livre

We show in detail that the limit of spherical surface integrals taken over slices of a high dimensional sphere is a Gaussian integral on an affine plane of finite codimension in infinite dimensional space. We then utilize these ideas to show that a natural class of orthogonal polynomials on high dimensional spheres limit to Hermite polynomials.