Proof of Tomaszewski's Conjecture on Randomly Signed Sums
N. Keller, and O. Klein. (2020)cite arxiv:2006.16834Comment: Light editorial changes. 76 pages.
Abstract
We prove the following conjecture, due to Tomaszewski (1986): Let $X=
\sum_i=1^n a_i x_i$, where $\sum_i a_i^2=1$ and each $x_i$ is a
uniformly random sign. Then $\Pr|X|1 1/2$. Our main novel tools are
local concentration inequalities and an improved Berry-Esseen inequality for
Rademacher sums.
Description
[2006.16834] Proof of Tomaszewski's Conjecture on Randomly Signed Sums
%0 Journal Article
%1 keller2020proof
%A Keller, Nathan
%A Klein, Ohad
%D 2020
%K mathematics randomness
%T Proof of Tomaszewski's Conjecture on Randomly Signed Sums
%U http://arxiv.org/abs/2006.16834
%X We prove the following conjecture, due to Tomaszewski (1986): Let $X=
\sum_i=1^n a_i x_i$, where $\sum_i a_i^2=1$ and each $x_i$ is a
uniformly random sign. Then $\Pr|X|1 1/2$. Our main novel tools are
local concentration inequalities and an improved Berry-Esseen inequality for
Rademacher sums.
@article{keller2020proof,
abstract = {We prove the following conjecture, due to Tomaszewski (1986): Let $X=
\sum_{i=1}^{n} a_{i} x_{i}$, where $\sum_i a_i^2=1$ and each $x_i$ is a
uniformly random sign. Then $\Pr[|X|\leq 1] \geq 1/2$. Our main novel tools are
local concentration inequalities and an improved Berry-Esseen inequality for
Rademacher sums.},
added-at = {2023-10-15T18:59:05.000+0200},
author = {Keller, Nathan and Klein, Ohad},
biburl = {https://www.bibsonomy.org/bibtex/29e98a8795d89d24a7a1a621f7b3db810/tabularii},
description = {[2006.16834] Proof of Tomaszewski's Conjecture on Randomly Signed Sums},
interhash = {4e912f553ee10963566655791f23fe71},
intrahash = {9e98a8795d89d24a7a1a621f7b3db810},
keywords = {mathematics randomness},
note = {cite arxiv:2006.16834Comment: Light editorial changes. 76 pages},
timestamp = {2023-10-15T18:59:05.000+0200},
title = {Proof of Tomaszewski's Conjecture on Randomly Signed Sums},
url = {http://arxiv.org/abs/2006.16834},
year = 2020
}