%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 }