Abstract Fourth Moment Theorems (Simon Campese -- University of Rome Tor Vergata)

Starts: 4:00 pm on Thursday, March 17, 2016
Ends: 5:00 pm on Thursday, March 17, 2016
Location: Math & Computer Science, Room 148, 111 Cummington Mall

Abstract: The classical Fourth Moment Theorem says that for a normalized sequence of multiple Wiener-It\^{o} integrals, convergence of just the fourth moment suffices to ensure convergence in law towards a standard Gaussian random variable. Since its discovery, several proofs and extensions of this result have been found, all of them heavily exploiting the rich structure of multiple integrals. In an exciting new development, it turned out that such Fourth Moment Theorems hold in much greater generality, namely for generic eigenfunctions of Markov diffusion generators with a certain chaotic property and target laws fulfilling some sufficient condition (examples being the Gaussian, Gamma and Beta distribution). We will present an overview of this new approach.