Comparing moments of real log-concave random variables.

Speaker(s)

Daniel Murawski

Affiliation

Uniwersytet Warszawski

Date

April 11, 2024, 12:15 p.m.

Room

room 3160

Seminar

Seminar of Probability Group

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Log-concave random variables play an important role in probability theory. Moment comparison inequalities of the form ∥X∥_p ≤ C_{p,q}∥X∥_q are particularly useful in concentration of measure and convex geometry. In this talk, I will present optimal bounds of the form ∥X∥p  ≤   C_{p, q} ∥X∥q for real log-concave random variables and show that for any p > q > 0 the maximum of the ratio ∥X∥_p /∥X∥_q is attained for some shifted exponential distribution.

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