Small-ball probabilities for mean widths of random polytopes

Speaker(s)

Eli Putterman

Affiliation

Tel Aviv University

Language of the talk

English

Date

March 6, 2025, 12:15 p.m.

Room

room 3160

Title in Polish

Small-ball probabilities for mean widths of random polytopes

Seminar

Seminar of Probability Group

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The classical theory of random polytopes addresses questions such as computing the expectation or variance of geometric parameters associated to a random polytope (e.g., volume, number of facets, or mean width); more recent theory also aims to obtain concentration of measure for such quantities. We study a question in random polytopes which current theory, surprisingly, does not address: bounding a high negative moment of the mean width of a certain random polytope, which requires bounding the probability that this mean width is a small fraction of its expectation ("small-ball estimates"). We will present, in some detail, the proofs of these small-ball estimates, which use different tools from those commonly employed in the field of random polytopes, and demonstrate an interesting phase transition in the behavior of the negative moment. If time permits, we will mention applications of this result to Sobolev inequalities.

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