Abstract
We show that a special setting of the well-known Gaussian correlation conjecture, namely for sets of equal measure, can be useful in proving the existence of small ball constants. We hope this sheds light on the conjecture and points out new directions for useful partial results. A simple proof for another useful correlation inequality needed in our argument is also presented.
Research partially supported by NSF Grant DMS-9972012.
Research partially supported by NSF Grant DMS-9802451.
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Li, W.V., Shao, QM. (2000). A Note on the Gaussian Correlation Conjecture. In: Giné, E., Mason, D.M., Wellner, J.A. (eds) High Dimensional Probability II. Progress in Probability, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1358-1_11
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DOI: https://doi.org/10.1007/978-1-4612-1358-1_11
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