Operator \ell_p to \ell_q norms of structured Gaussian matrices

Speaker(s)

Rafał Latała

Affiliation

Uniwersytet Warszawski

Language of the talk

English

Date

Oct. 17, 2024, 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

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We discuss two-sided bounds for operator \ell_p to \ell_q norms of structured Gaussian matrices in the case 1\le p\le 2\le q\leq \infty. Guédon, Hinrichs, Litvak and Prochno conjectured that an easy lower bound for the expected value may be reversed up to a multiplicative constant depending only on p and q. We verify the conjecture in the range $p^*,q\in [2,4)$ and show that it holds  up to a loglog factor in the remaining  range.

(based on a joint work in progress with Marta Strzelecka)

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We discuss two-sided bounds for operator \ell_p to \ell_q norms of structured Gaussian matrices in the case 1\le p\le 2\le q\leq \infty. Guédon, Hinrichs, Litvak and Prochno conjectured that an easy lower bound for the expected value may be reversed up to a multiplicative constant depending only on p and q. We verify the conjecture in the range $p^*,q\in [2,4)$ and show that it holds  up to a loglog factor in the remaining  range.

(based on a joint work in progress with Marta Strz

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