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Random symmetric polynomials

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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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Literature cited

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Additional information

Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 170–188, 1986.

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Zolotarev, V.M. Random symmetric polynomials. J Math Sci 38, 2262–2272 (1987). https://doi.org/10.1007/BF01093827

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  • Limit Theorem
  • General Assumption
  • Symmetric Polynomial
  • Obtain Limit Theorem