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arXiv · 2109.07375

Lyapunov exponents for truncated unitary and Ginibre matrices

Andrew Ahn·Roger Van Peski
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Abstract

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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Andrew Ahn, Roger Van Peski. 2021-09-15. Lyapunov exponents for truncated unitary and Ginibre matrices. https://arxiv.org/abs/2109.07375

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