Symmetric Gaussian Rearrangement with Applications to Gaussian Noise Stability
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Authors
Baker, Graeme
Date
Type
thesis
Language
eng
Keyword
Noise stability , Gaussian measure , Symmetric sets , Rearrangement
Alternative Title
Abstract
We introduce a new symmetric Gaussian rearrangement that applies to sets and functions which are invariant with respect to a given finite subgroup of the orthogonal group. The properties of this rearrangement are developed, connecting it with the existing theory, and we show that the Hardy--Littlewood inequality holds for this rearrangement. As an application, certain integrals involving the Ornstein--Uhlenbeck semigroup are shown to be non-decreasing under rearrangement of their initial data. This in turn demonstrates a new form of Borell's inequality: the (positive correlation) Gaussian noise stability of a set is non-decreasing under appropriate symmetric Gaussian rearrangement.
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This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.