Submitted Abstract
The research described in this proposal provides new and fresh perspectives for the Malliavin-Stein approach, at the boundary of different mathematical fields such as probability, functional analysis and geometry. It is also expected that the new findings it will generate will have a scope of applications that goes far beyond the framework of the present project, with ramifications both in applied and pure mathematics. To be more specific, in this project it is intended among others to:(i) understand in depth the nature and properties of limit of multiple stochastic integrals, these latter being the building blocks of any square integrable functional of a Gaussian process;(ii) thoroughly analyse the phase transition that occurs in the context of large Gaussian correlated Wishart matrices;(iii) study a number of conjectures attached to the intrinsic volumes of cones and of convex bodies, a concept at the boundary of several mathematical fields;(iv) explore new venues towards the solution of the famous and long-standing Gaussian product conjecture.