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* Princeton Discrete Math Seminar *
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Speaker: Ohad Klein (Bar Ilan University)
Thursday March 3, 3:00 via Zoom.
Title: On the distribution of randomly signed sums and Tomaszewski’s
conjecture
A Rademacher sum X is a random variable characterized by real numbers
a_1,..., a_n, and is equal to X = a_1 x_1 + ... + a_n x_n, where x_1, ..., x_n
are independent signs (uniformly selected from {-1, 1}).
A conjecture by Bogusław Tomaszewski, 1986:
All Rademacher sums X satisfy Pr[ |X| <= sqrt Var(X) ] >= 1/2.
We prove the conjecture, and discuss other ways in which Rademacher sums
behave like normally distributed variables.
Joint work with Nathan Keller.
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Next week: TBA
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