Anti-concentration with respect to random permutations

Aaron Berger; Ross Berkowitz; Pat Devlin; Van Vu

paper

Anti-concentration with respect to random permutations

arXiv:2601.04384

Abstract

Classical anti-concentration results focus on the random sum $S := \sum_{i = 1}^{n} I^¾_{i} v_{i}$ , where $I^¾_{i}$ are independent random variables and $v_{i}$ are real numbers. In this paper, we prove new concentration results concerning the random sum $S := \sum_{i = 1}^{n} w_{I ¨ _{i}} v_{i}$ , where $w_{i}, v_{i}$ are real numbers and $I ¨ $ is a random permutation.