Our colloquium takes place on the first Tuesday of each month from 15:30 to 16:30, usually in room A709.
A renowned expert (being an excellent speaker as well) visits us for an afternoon and gives a panorama of one of her research areas. The talk is meant to be accessible to all members of the lab, including PhD students in analysis, game theory, probability and statistics. Ideally, it should start gently with an historical background on the problem and an overview of the main questions and applications, keeping a non technical style during at least the first half of the talk. Of course it is also nice to have a part with more mathematical details: the most appreciated colloquia were those in which the speaker succeeded to develop a nice technical idea or an elegant argument that everyone should know.
Food and drinks are served after the event, usually in Espace 7!
Date: Tuesday, May 5th 2026 (15:30-16:30, room A709)
Title: Large covariance matrices, eigenvector overlaps & “fleeting modes”: a (free) RMT approach
Abstract: We will how discuss free Random Matrix Theory allows one to understand the overlap of the eigenvectors of noisy covariance matrices with their underlying "true" counterparts, with direct applications to financial data analysis. Using matrix subordination laws derived from replica methods, we compute explicit overlaps between eigenvectors of pure and noise-perturbed matrices in both additive and multiplicative noise scenarios. These universal results—independent of specific matrix distributions—enable remarkable "large dimension miracles": optimal estimators of unknown covariance matrices can be constructed knowing only observed data, and statistical tests for stationarity can be performed without knowing the true underlying correlation structure. We demonstrate practical applications to portfolio optimization through non-linear shrinkage estimators and introduce "fleeting modes"—a novel diagnostic test identifying unstable eigenvector directions driven by market microstructure and behavioral effects. Finally, we explore time-dependent correlations in financial markets, revealing how principal regression analysis combined with RMT reveals which macroeconomic factors systematically influence asset correlations across market regimes.