Operator-norm Sudakov minoration for Gaussian chaos of order two

Prelegent(ci)

Witold Bednorz

Afiliacja

University of Warsaw

Język referatu

angielski

Termin

29 października 2026 12:15

Pokój

p. 3160

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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For a family of matrices separated in operator norm, must the expected supremum of the associated bilinear Gaussian process be at least the separation times the square root of the logarithm of the family size? This is the question asked in Talagrand’s Research Problem 15.1.16 (Decomposition Book). We explain the proof of the result. The central estimate treats moving singular directions jointly through an adaptive Gaussian experiment. A weighted posterior entropy pays for the information recovered at every stage. Convex separation and a dual Gaussian cover then provide a result in a common row space. Choosing the correct operator scale before compressing the original matrices completes the endpoint argument.

(AI was used in this research)

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