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SUMMARY:Tight anti-concentration of Rademacher sums - Lawrence Hollom (Cam
 bridge)
DTSTART:20240516T133000Z
DTEND:20240516T143000Z
UID:TALK216919@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:We consider lower bounds on anti-concentration probabilities o
 f\nthe form P(|X| >= x)\, where X = a_1 ε_1 + ... + a_n ε_n is a Rademac
 her\nsum\; ε_i are independent and uniform signs +1 or -1\, and a_i > 0 a
 re\nconstants normalised so that Var(X) = 1. We determine the infimal valu
 e of\nP(|X| >= x) over Rademacher sums X for all values x >= 0\, giving a 
 partial\nanswer to a question by Keller and Klein. In particular\, for x =
  1 we\nimprove on a sequence of results to produce the optimal lower bound
  P(|X|\n>= 1) >= 7/32\, confirming a conjecture of Hitczenko and Kwapień.
LOCATION:MR12
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