שלחו לחבר

On the distribution of randomly signed sums and Tomaszewski’s conjecture

Seminar
Speaker
Ohad Klein (Bar-Ilan University)
Date
10/01/2021 - 15:30 - 14:00
Place
Zoom
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, 
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.

תאריך עדכון אחרון : 05/01/2021