A Three Dimensional Signed Small Ball Inequality

The Small Ball Inequality is a conjectural lower bound on sums the L-infinity norm of sums of Haar functions supported on dyadic rectangles of a fixed volume in the unit cube. The conjecture is fundamental to questions in discrepancy theory, approximation theory and probability theory. In this artic...

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Bibliographic Details
Published in:arXiv.org 2010-01
Main Authors: Bilyk, Dmitriy, Lacey, Michael T, Parissis, Ioannis, Vagharshakyan, Armen
Format: Article
Language:English
Subjects:
Economic models
Lower bounds
Probability theory
Rectangles
Sums
Online Access:Get full text
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Summary:The Small Ball Inequality is a conjectural lower bound on sums the L-infinity norm of sums of Haar functions supported on dyadic rectangles of a fixed volume in the unit cube. The conjecture is fundamental to questions in discrepancy theory, approximation theory and probability theory. In this article, we concentrate on a special case of the conjecture, and give the best known lower bound in dimension 3, using a conditional expectation argument.
ISSN:2331-8422