A Systematic Martingale Construction With Applications to Permutation Inequalities

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Construction of martingales
permutation inequalities
garsia inequality
combinatorial martingales; Discrete Brownian bridge
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Set Theory
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Pozdnyakov, Vladimir
Steele, John M
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We illustrate a process that constructs martingales with help from matrix products that arise naturally in the theory of sampling without replacement. The usefulness of the new martingales is illustrated by the development of maximal inequalities for permuted sequences of real numbers. Some of these inequalities are new and some are variations of classical inequalities like those introduced by A. Garsia in the study of rearrangement of orthogonal series.

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2013-11-01
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Journal of Mathematical Analysis and Applications
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