3 papers
math.FA2025
Operator-valued Khintchine inequality for -free semicircles
Benoît Collins, Akihiro Miyagawa
We exhibit several bounds for operator norms of the sum of -free semicircular random variables introduced in the paper of Speicher and WysoczaÅski. In particular, using the fi…
q-fin.ST2025
Holdout cross-validation for large non-Gaussian covariance matrix estimation using Weingarten calculus
Lamia Lamrani, Benoît Collins, Jean-Philippe Bouchaud
Cross-validation is one of the most widely used methods for model selection and evaluation; its efficiency for large covariance matrix estimation appears robust in practice, but li…
math.OA2025
Variations on quantum de Finetti theorems and operator valued Martin boundaries: a Choquet-Deny approach
Benoît Collins, Thierry Giordano, Ryosuke Sato
We revisit the quantum de Finetti theorem. We state and prove a couple of variants thereof. In parallel, we introduce an operator version of the Martin boundary on quantum groups a…