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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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