Tight anti-concentration of Rademacher sums

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• Lawrence Hollom (Cambridge)
• Thursday 16 May 2024, 14:30-15:30
• MR12.

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We consider lower bounds on anti-concentration probabilities of the form P(|X| >= x), where X = a_1 ε_1 ... a_n ε_n is a Rademacher sum; ε_i are independent and uniform signs +1 or -1, and a_i > 0 are constants normalised so that Var(X) = 1. We determine the infimal value of P(|X| >= x) over Rademacher sums X for all values x >= 0, giving a partial answer to a question by Keller and Klein. In particular, for x = 1 we improve on a sequence of results to produce the optimal lower bound P(|X| >= 1) >= 7/32, confirming a conjecture of Hitczenko and Kwapień.

This talk is part of the Combinatorics Seminar series.

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