Anticoncentration of random vectors via the strong perfect graph theorem

0580826 - ÚI 2024 eng V - Výzkumná zpráva
Juškevičius, Tomas - Kurauskas, V.
Anticoncentration of random vectors via the strong perfect graph theorem.
Cornell University: Cornell University, 2023. 34 s. arXiv.org e-Print archive, arXiv:2306.11904.
Grant CEP: GA ČR(CZ) GJ20-27757Y
Institucionální podpora: RVO:67985807
Klíčová slova: concentration function * Littlewood-Offord problem * perfect graph
https://arxiv.org/abs/2306.11904

In this paper we give anticoncentration bounds for sums of independent random vectors in finite-dimensional vector spaces. In particular, we asymptotically establish a conjecture of Leader and Radcliffe (1994) and a question of Jones (1978). The highlight of this work is an application of the strong perfect graph theorem by Chudnovsky, Robertson, Seymour and Thomas (2003) in the context of anticoncentration.
Trvalý link: https://hdl.handle.net/11104/0349588