Non-abelian Littlewood–Offord inequalities

Pham H. Tiep; Van H. Vu

doi:10.1016/j.aim.2016.08.002

Non-abelian Littlewood–Offord inequalities

Pham H. Tiep, Van H. Vu

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In 1943, Littlewood and Offord proved the first anti-concentration result for sums of independent random variables. Their result has since then been strengthened and generalized by generations of researchers, with applications in several areas of mathematics. In this paper, we present the first non-abelian analogue of the Littlewood–Offord result, a sharp anti-concentration inequality for products of independent random variables.

Original language	English (US)
Pages (from-to)	1233-1250
Number of pages	18
Journal	Advances in Mathematics
Volume	302
DOIs	https://doi.org/10.1016/j.aim.2016.08.002
State	Published - Oct 22 2016

Keywords

Anti-concentration inequalities
Littlewood–Offord–Erdős theorem

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2016.08.002

Cite this

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AB - In 1943, Littlewood and Offord proved the first anti-concentration result for sums of independent random variables. Their result has since then been strengthened and generalized by generations of researchers, with applications in several areas of mathematics. In this paper, we present the first non-abelian analogue of the Littlewood–Offord result, a sharp anti-concentration inequality for products of independent random variables.

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KW - Littlewood–Offord–Erdős theorem

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ER -

Non-abelian Littlewood–Offord inequalities

Abstract

Keywords

ASJC Scopus subject areas

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