Expected Supremum of a Random Linear Combination of Shifted Kernels
Information Theory
2012-08-28 v1 math.IT
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.
Keywords
Cite
@article{arxiv.1208.5281,
title = {Expected Supremum of a Random Linear Combination of Shifted Kernels},
author = {Holger Boche and Brendan Farrell and Michel Ledoux and Moritz Wiese},
journal= {arXiv preprint arXiv:1208.5281},
year = {2012}
}
Comments
To appear in the Journal of Fourier Analysis and Applications