Korolyuk, V. S.; Borovskikh, Yu. V. A random symmetric polynomial with increasing degree. (Russian. English summary) Zbl 0711.60021 Dokl. Akad. Nauk Ukr. SSR, Ser. A 1990, No. 4, 10-13 (1990). Elementary symmetric polynomials of i.i.d. random variables with finite variance are considered. Non-normal limit distributions are found in the case where the degree of the polynomials tends to infinity more slowly than the number of variables. Reviewer: T.F.Mori MSC: 60F05 Central limit and other weak theorems 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:Hermite polynomials; symmetric polynomials; normal limit distributions PDFBibTeX XMLCite \textit{V. S. Korolyuk} and \textit{Yu. V. Borovskikh}, Dokl. Akad. Nauk Ukr. SSR, Ser. A 1990, No. 4, 10--13 (1990; Zbl 0711.60021)