Lyapunov exponents for truncated unitary and Ginibre matrices

2021/09/15 by Ahn, Andrew, Van Peski, Roger · 3 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2109.07375

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 GL_n(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.

Cited by

• Global and local limits for products of rectangular Ginibre matrices
• Edge statistics for singular values of products of rectangular complex Ginibre matrices
• Local Statistics of Singular Values for Products of Truncated Unitary Matrices

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