关于$SU(2)$上Rudin-Shapiro多项式的分布和缺环游动
On the distribution of Rudin-Shapiro polynomials and lacunary walks on $SU(2)$
摘要：
我们的特点的极限分布的鲁丁-夏皮罗多项式，表明，归一化，其值成为均匀分布在光盘。这解决了萨法里和蒙哥马利的问题。我们的证明收益有关的多项式的分布，弱相依随机矩阵的产品，我们分析使用$SU(2)$的表示论。我们的方法使我们的非交换模拟的经典中心极限定理的塞勒姆和Zygmund，这可能是独立的利益。
英文摘要：
We characterize the limiting distribution of Rudin-Shapiro polynomials, showing that, normalized, their values become uniformly distributed in the disc. This resolves conjectures of Saffari and Montgomery. Our proof proceeds by relating the polynomials' distribution to that of a product of weakly dependent random matrices, which we analyze using the representation theory of $SU(2)$. Our approach leads us to a non-commutative analogue of the classical central limit theorem of Salem and Zygmund, which may be of independent interest.
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