截断酉矩阵和Ginibre矩阵的Lyapunov指数

IF 1.5 Q2 PHYSICS, MATHEMATICAL
Andrew Ahn, Roger Van Peski
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引用次数: 5

摘要

在本文中,我们证明了随机截断Haar酉矩阵和复Ginibre矩阵的混合积的Lyapunov指数是由等间距的“尖桩栅栏”统计量渐近给出的。我们讨论了这些统计量是如何从$\operatorname{GL}_n(\mathbb{C})$上的随机矩阵乘积和乘法布朗运动之间的联系中产生的,类似于离散随机游动和普通布朗运动之间的联系。我们的方法是基于可积概率的经典矩阵系积的轮廓积分公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lyapunov exponents for truncated unitary and Ginibre matrices
In this note, we show that the Lyapunov exponents of mixed products of random truncated Haar unitary and complex Ginibre matrices are asymptotically given by equally spaced `picket-fence' statistics. We discuss how these statistics should originate from the connection between random matrix products and multiplicative Brownian motion on $\operatorname{GL}_n(\mathbb{C})$, analogous to the connection between discrete random walks and ordinary Brownian motion. Our methods are based on contour integral formulas for products of classical matrix ensembles from integrable probability.
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CiteScore
2.30
自引率
0.00%
发文量
16
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