pr.probability – Uniform convergence of random Fourier quadratic forms

Let $xi_k$, $k in mathbb {Z}$, be a sequence of independent Rademacher random variables. Is there
a characterization of those families $a_{k,ell}$, $k, ell in mathbb {Z}$, of complex numbers such that the quadratic form
sum_{k, ell in mathbb {Z}} a_{k, ell} , xi_k xi_ell , e^{itk} e^{isell}, quad t,s in [0, 2pi],

is almost surely uniformly convergent?