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Published August 2012 | Submitted
Journal Article Open

Expected Supremum of a Random Linear Combination of Shifted Kernels

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 √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 √n log n for all reasonable coefficient statistics.

Additional Information

© 2012 Springer Science+Business Media, LLC. Received: 20 June 2011; Revised: 15 December 2011; Published online: 3 February 2012. H. Boche was supported by start-up funds of the Technische Universität München.

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