Optimal constants C_{p, 4} in Khintchine inequality

Speaker(s)

Daniel Murawski

Affiliation

Uniwersytet Warszawski

Language of the talk

English

Date

Dec. 19, 2024, 12:15 p.m.

Room

room 3160

Title in Polish

Optimal constants C_{p, 4} in Khintchine inequality

Seminar

Seminar of Probability Group

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We prove that whenever S is a weighted sum of n independent Rademacher random variables, then ||S||_p / ||S||_4 \leq ||G||_p / ||G||_4, where G is a standard Gaussian random variable and p \geq 4. Moreover, we prove that for fixed n and p \geq 5, the maximum is attained in a case where all, except at most one, coefficients of Rademacher sum are equal. As a corollary of the main result, we show that ||S||_p \leq (1 - \Omega(1/n))||G||_p and 1/n is the optimal order in such an estimate.

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