Abstract
Let {Q(n)(x1,...,xn)} be a sequence of symmetric polynomials having a fixed degree equal to k. Let {Xn1,...,Xnn}, n⩾ k, be some sequence of series of random variables (r.v.). We form the sequence of r.v. Yn=Q(n)(Xn1, ... Xnn), n⩾ k One obtains limit theorems for the sequence Yn, under very general assumptions.
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