On the distribution of randomly signed sums and Tomaszewski’s conjecture
Seminar
Speaker
Ohad Klein (Bar-Ilan University)
Date
10/01/2021 - 15:30 - 14:00Add to Calendar
2021-01-10 14:00:00
2021-01-10 15:30:00
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}).
We discuss various aspects in which Rademacher sums behave "somewhat" like normally distributed variables.
A relevant puzzle by Bogusław Tomaszewski, 1986:
Is it true that all Rademacher sums X satisfy Pr[ |X| <= sqrt Var(X) ] >= 1/2 ?
(for normally distributed variables, Pr ~ 0.68)
Joint work with Nathan Keller.
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אוניברסיטת בר-אילן - Department of Mathematics
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Asia/Jerusalem
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Abstract
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,
X = a_1 x_1 + ... + a_n x_n,
where x_1, ..., x_n are independent signs (uniformly selected from {-1, 1}).
We discuss various aspects in which Rademacher sums behave "somewhat" like normally distributed variables.
A relevant puzzle by Bogusław Tomaszewski, 1986:
Is it true that all Rademacher sums X satisfy Pr[ |X| <= sqrt Var(X) ] >= 1/2 ?
We discuss various aspects in which Rademacher sums behave "somewhat" like normally distributed variables.
A relevant puzzle by Bogusław Tomaszewski, 1986:
Is it true that all Rademacher sums X satisfy Pr[ |X| <= sqrt Var(X) ] >= 1/2 ?
(for normally distributed variables, Pr ~ 0.68)
Joint work with Nathan Keller.
Joint work with Nathan Keller.
Last Updated Date : 05/01/2021
