Low Correlation Noise Stability of Symmetric Sets

Steven Heilman ()
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Steven Heilman: University of Southern California

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 2192-2240

Abstract: Abstract We study the Gaussian noise stability of subsets A of Euclidean space satisfying $$A=-A$$ A = - A . It is shown that an interval centered at the origin, or its complement, maximizes noise stability for small correlation, among symmetric subsets of the real line of fixed Gaussian measure. On the other hand, in dimension two and higher, the ball or its complement does not always maximize noise stability among symmetric sets of fixed Gaussian measure. In summary, we provide the first known positive and negative results for the symmetric Gaussian problem.

Keywords: Noise stability; Symmetric sets; Gaussian measure; Optimization; Calculus of variations; 60E15; 49Q10; 46N30 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01031-y

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