Non-abelian Littlewood–Offord inequalities

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Author
Tiep, Pham H.
Vu, Van H.
Affiliation
Univ Arizona, Dept Math
Issue Date
2016-10
Keywords
Littlewood-Offord-Erdos theorem
Anti-concentration inequalities

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Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
Non-abelian Littlewood–Offord inequalities 2016, 302:1233 Advances in Mathematics
Journal
Advances in Mathematics
Rights
© 2016 Elsevier Inc. All rights reserved.
Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
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 generalised 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. (C) 2016 Elsevier Inc. All rights reserved.
Note
Available online 30 September 2016; 24 month embargo
ISSN
00018708
DOI
10.1016/j.aim.2016.08.002
Version
Final accepted manuscript
Sponsors
NSF [DMS-1201374]; Simons Foundation Fellowship [305247]; [DMS-0901216]; [AFOSAR-FA-9550-09-1-0167]
Additional Links
http://linkinghub.elsevier.com/retrieve/pii/S0001870816309859
https://arxiv.org/abs/1506.01958
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