Dr. Marwa Banna
Dr. Tobias Mai

Seminar on Gaussian Hilbert Spaces

(Summer Semester 2020)


Time and Place

Wednesday, 10:00 - 11:30    (online, via the platform Zoom)


Gaussian Hilbert spaces are Hilbert spaces consisting of centered Gaussian random variables. Accordingly, Gaussian Hilbert spaces are located at the intersection of probability and Hilbert space theory and turn out to have a rich and powerful structure with various applications. Gaussian Hilbert spaces and related concepts appear, for instance, in stochastic analysis and in quantum field theory and have applications even outside probability theory like in Banach space geometry and in the area of partial differential equations.

In this seminar, we want to give an introduction to the theory of Gaussian Hilbert spaces following the identically named book by Svante Janson. We will discuss the main pillars of that subject, including the Wiener chaos decomposition, Wick products, the Fock space and the hypercontractivity phenomenon, as well as some of the beautiful applications in stochastic integration, Malliavin calculus, U-Statistics and operator theory.

Seminar announcement

For further information, please contact Marwa Banna or Tobias Mai.



updated: 6 July 2020   Tobias Mai