Operator-norm Sudakov minoration for Gaussian chaos of order two

Speaker(s)

Witold Bednorz

Affiliation

University of Warsaw

Language of the talk

English

Date

Oct. 29, 2026, 12:15 p.m.

Room

room 3160

Seminar

Seminar of Probability Group

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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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