Nongaussian Limit Distributions of Lacunary Trigonometric Series

It is a well known fact that for rapidly increasing nkthe sequence , behaves like a sequence of independent random variables; in particular has a limiting Gaussian distribution as N → ∞. Under a certain critical speed this result breaks down and becomes strongly dependent. The purpose of this paper is to investigate the asymptotic behavior of normed sums in the strongly dependent domain; specifically, we construct a large class of nongaussian limit distributions of such sums.