The best constant in the Khinchine inequality for slightly dependent random variables
Orli Herscovici, Susanna Spektor
TL;DR
This paper determines the optimal constant in the Khintchine inequality specifically for sums of Rademacher variables constrained to sum to zero, advancing understanding of inequalities under dependence.
Contribution
It provides the first precise calculation of the best constant in the Khintchine inequality for dependent Rademacher variables with zero sum constraint.
Findings
Identifies the exact best constant for the inequality under the given dependence.
Extends classical Khintchine inequality to a dependent setting.
Offers insights into inequalities involving constrained random variables.
Abstract
We compute the best constant in the Khintchine inequality under assumption that the sum of Rademacher random variables is zero.
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Taxonomy
TopicsPoint processes and geometric inequalities · Random Matrices and Applications · advanced mathematical theories