Central limit theorems have played a central role in the development of probability theory and mathematical statistics; they also appear in various other places such as in number theory (e.g. Selberg's limit theorem for the Riemann zeta function), in random matrix theory, in representation theory, in the study of combinatorial structures, etc. One often looks for the relevant normalization of the underlying sequence of random variables in order to establish convergence in distribution to, say, the Gaussian distribution. We shall see in this talk how one obtains more information and more refined results if one rather tries to find a "good" normalization for the Fourier transform of the underlying sequence of probability distributions. This will lead us to introduce a new mode of convergence, called mod-* convergence, together with some non-trivial consequences. We shall illustrate this with diverse examples from probability theory, number theory and random matrix theory. In particular we shall try to understand with a different point of view some of the recent conjectures in number theory coming from random matrix theory.
Donnerstag, den 17. November 2011 um 17 Uhr c.t. Uhr, in INF 288, HS2 Donnerstag, den 17. November 2011 at 17 Uhr c.t., in INF 288, HS2
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Mark Podolskij