CMV matrices in random matrix theory and integrable systems: a survey
Irina Nenciu
TL;DR
This survey explores CMV matrices, highlighting their significance in random matrix theory and integrable systems, and drawing parallels with Jacobi matrices to unify various mathematical frameworks.
Contribution
It provides a comprehensive overview of recent developments involving CMV matrices and their applications in random matrices and integrable systems, emphasizing their connections to Jacobi matrices.
Findings
CMV matrices are crucial in understanding spectral properties of random matrices.
Connections between CMV and Jacobi matrices reveal underlying structural similarities.
Recent results demonstrate the versatility of CMV matrices in integrable systems.
Abstract
We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems. Throughout the paper we also emphasize the analogies and connections to Jacobi matrices.
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