自由随机变量齐次和的不变性原理
概率论
2014-03-11 v3 算子代数
摘要
在自由概率框架下，我们推广了最近在 [E. Mossel, R. O'Donnell and K. Oleszkiewicz (2010). Noise stability of functions with low influences: invariance and optimality. {\it Ann. Math.} {\bf 171}, no. 1, 295-341] 中建立的一个关于低影响度多重线性齐次和的不变性原理。为此，这些齐次和的超压缩性质是必需的，而证明该性质已成为我们的主要任务。最后，我们从推广中推导出了若干普适性现象，其精神与论文 [I. Nourdin, G. Peccati and G. Reinert (2010). Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos. {\it Ann. Probab.} {\bf 38}, no. 5, 1947-1985] 相一致。
引用
@article{arxiv.1201.1753,
title = {Invariance principles for homogeneous sums of free random variables},
author = {Aurélien Deya and Ivan Nourdin},
journal= {arXiv preprint arXiv:1201.1753},
year = {2014}
}
备注
Published in Bernoulli (http://dx.doi.org/10.3150/12-BEJ498) by the International Statistical Institute/Bernoulli Society