Expected Supremum of a Random Linear Combination of Shifted Kernels

Holger Boche; Brendan Farrell; Michel Ledoux; Moritz Wiese

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arXiv · 1208.5281

Expected Supremum of a Random Linear Combination of Shifted Kernels

Holger Boche·Brendan Farrell·Michel Ledoux·Moritz Wiese

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Abstract

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order \sqrt{\log n}, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order \log\log n. This is a noteworthy difference to orthonormal functions on the unit interval, where the expected supremum is of order \sqrt{n\log n} for all reasonable coefficient statistics.

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Holger Boche, Brendan Farrell, Michel Ledoux, Moritz Wiese. 2012-08-27. Expected Supremum of a Random Linear Combination of Shifted Kernels. https://arxiv.org/abs/1208.5281

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