Expected Supremum of a Random Linear Combination of Shifted Kernels

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.