@inproceedings{ac42583b3c604cd0be8c2d594eb6cf1a,
title = "Local Concentration Inequalities and Tomaszewski{\textquoteright}s Conjecture",
abstract = "We prove Tomaszewski's conjecture (1986): Let f:\{-1,1\}n ? R be of the form f(x)= ?i=1n ai xi. Then Pr[|f(x)| ? Var[f]] ? 1/2. Our main novel tools are local concentration inequalities and an improved Berry-Esseen inequality for first-degree functions on the discrete cube. These tools are of independent interest, and may be useful in the study of linear threshold functions and of low degree Boolean functions.",
keywords = "Combinatorics, Probabilistic Inequalities, Tail Inequalities",
author = "Nathan Keller and Ohad Klein",
note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 ; Conference date: 21-06-2021 Through 25-06-2021",
year = "2021",
month = jun,
day = "15",
doi = "10.1145/3406325.3451011",
language = "الإنجليزيّة",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
pages = "1656--1669",
editor = "Samir Khuller and Williams, \{Virginia Vassilevska\}",
booktitle = "STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing",
}