Colloquium du CEREMADE

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Intervenant : ()
Titre :


Le : 05/05/2026 de : 15:30 à : 16:30

Salle :

Colloquium du CEREMADE

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Intervenant : BOUCHAUD Jean-Philippe (CFM)
Titre :
Large covariance matrices, eigenvector overlaps & “fleeting modes”: a (free) RMT approach

Le : 05/05/2026 de : 15:30 à : 16:30
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.
Salle : A709