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Low Correlation Noise Stability of Symmetric Sets

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  • Steven Heilman

    (University of Southern California)

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.

Suggested Citation

  • Steven Heilman, 2021. "Low Correlation Noise Stability of Symmetric Sets," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2192-2240, December.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:4:d:10.1007_s10959-020-01031-y
    DOI: 10.1007/s10959-020-01031-y
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    References listed on IDEAS

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    1. T. Matsunawa, 1976. "Some inequalities based on inverse factorial series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 291-305, December.
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