ABSTRACT
We use properties of vector-valued gaussian random functions to study the behavior of https://www.w3.org/1998/Math/MathML">supα∈[0,1]supN∈ℕ|[Nlog(pN+1+logN)]−1/2∑k=0Nθkexp[i2πpkα]|https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332838/58f4c041-1317-4a7c-b51a-e794ca13209e/content/eq1578.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
where {θk, k ∈ ℕ} is a sequence of I.I.D. symmetric L2–random variables and {pk, k ∈ ℕ} is an increasing positive sequence. Some previous author used trigonometric methods to obtain similar results ; the given proof is typical for using Gaussian methods.
