Operator \ell_p to \ell_q norms of structured Gaussian matrices

Speaker(s)

Marta Strzelecka

Affiliation

University of Warsaw

Language of the talk

English

Date

Feb. 27, 2025, 12:15 p.m.

Room

room 3160

Title in Polish

Operator \ell_p to \ell_q norms of structured Gaussian matrices

Seminar

Seminar of Probability Group

---

We report the progress in two-sided bounds for operator norms from \ell_p to \ell_q of structured Gaussian matrices in the case when p^*,q>=2. Guédon, Hinrichs, Litvak and Prochno conjectured that in this range an easy lower bound for the expected value of p \to q norm may be reversed up to a multiplicative constant depending only on p and q. We confirm this conjecture in the ranges p^*,q\in [2,4) (covered in a previous talk) and p^*,q>2. Moreover, in the missing boundary cases, when p^*=2 and q>=4 (or, dually, when q=2 and 4>=p^*), we confirm the conjecture up to a factor of order log(log(mn)).

The talk will be a continuation of the talk given by Rafał Latała on October 17th, 2024. We will recall all the necessary  notation, previously known results, etc., so the talk will be accessible for everyone and there is no need to remember the content of the previous lecture.

(based on a joint work with Rafał Latała)

---