Operator \ell_p to \ell_q norms of structured Gaussian matrices

Prelegent(ci)

Rafał Latała

Afiliacja

Uniwersytet Warszawski

Język referatu

angielski

Termin

17 października 2024 12:15

Pokój

p. 3160

Tytuł w języku polskim

Operator \ell_p to \ell_q norms of structured Gaussian matrices

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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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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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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