Colloquium Mathematics - Giovanni Peccati, University of Luxembourg

As part of the Workshop On Randomness and Discrete Structures (WORDS2025) Givovanni Peccati gives the following colloquium:

Title: On irreducible CLTs

Abstract:

Central limit theorems (CLTs) for homogeneous sums (or, more generally, degenerate U-statistics) of independent random variables are classical results in modern stochastic analysis, that have been recently refined and considerably extended through the use of Malliavin calculus and associated variational tools. The aim of this talk is to address the following question: 'Can one characterize those CLTs for homogeneous sums that cannot be reduced to the classical Lindberg principle?' I will provide several partial answers to this question, based on the use of Laplace spectra for (hyper)graphs, Cheeger inequalities, as well as a certain notion of "combinatorial dimension" introduced in a seminal book by R. Blei (2001).

Based on a joint work with F. Caravenna and F. Cottini.