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SUMMARY:Ohad Klein (Bar-Ilan University)
DTSTART:20210208T200000Z
DTEND:20210208T210000Z
DTSTAMP:20260423T021335Z
UID:paw/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/paw/18/">On 
 the distribution of Randomly Signed Sums and Tomaszewski’s Conjecture</a
 >\nby Ohad Klein (Bar-Ilan University) as part of Probability and Analysis
  Webinar\n\n\nAbstract\nA Rademacher sum $X$ is a random variable characte
 rized by real numbers $a_1\, \\ldots\, a_n$\, and is equal to\n\n$$X = a_1
  x_1 + \\ldots + a_n x_n\,$$ where $x_1\, \\ldots\, x_n$ are independent s
 igns (uniformly selected from $\\{-1\, 1\\}$).\n\nA conjecture by Bogusła
 w Tomaszewski\, 1986: all Rademacher sums $X$ satisfy $$\\textup{Pr}[ |X| 
 \\leq  \\sqrt {\\textup{Var}(X)} ] \\geq 1/2$$\n\nWe prove the conjecture\
 , and discuss other ways in which Rademacher sums behave like normally dis
 tributed variables.\n\nJoint work with Nathan Keller.\n
LOCATION:https://researchseminars.org/talk/paw/18/
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