Random symmetric polynomials (Q1117573)

[For the entire collection see Zbl 0626.00025.] Let \(\{Q^{(n)}(x_ 1,...,x_ n)\}\) be a sequence of symmetric polynomials having a fixed degree equal to k. Let \(\{X_{n1},...,X_{nn}\}\), \(n\geq k\), be some sequence of series of random variables (r.v.). We form the sequence of r.v. \[ y_ n=Q^{(n)}(X_{n1},...,X_{nn}),\quad n\geq k. \] Limit theorems for the sequence \(y_ n\) under very general assumptions are obtained.