期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2012
卷号：IX
页码：101-127
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：If x and y are two free semicircular random variables in a non-commuta-tive probability space (A,E) and have variance one, we call the law of 1 p2(xy +yx)the tetilla law (and we denote it by T ), because of the similarity between the formof its density and the shape of the tetilla cheese from Galicia. In this paper, weprove that a unit-variance sequence {Fn} of multiple Wigner integrals converges indistribution to T if and only if E[F4n] ! E[T 4] and E[F6n] ! E[T 6]. This resultshould be compared with limit theorems of the same flavor, recently obtained byKemp et al. (2012) and Nourdin and Peccati (2011).
