Intrinsic volumes and Gaussian processes (Q2749126)

Intrinsic volumes or quermassintegrals reflect key properties of convex bodies. In the present paper they are related to questions of regularity of a Gaussian process \(X\) associated with the body \(K\) by \(X_t=\sum t_iZ_i\), where \(t\in K\) and \(Z_1, Z_2, \ldots\) are i.i.d. standard Gaussian variables. The paper can be read either as a detailed study of random convex sets of the form \(M\cdot K\), where \(K\) is a fixed convex body and \(M\) a matrix with iid Gaussian entries, or as a study of the extension of intrinsic volumes to convex bodies in infinite dimensions given in probabilistic terms.