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<p>This paper calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can give a complete algorithm for computing the fluctuations. When multiple eigenvalues are involved, we present several examples suggesting that a general algorithm would be much more complex.</p>

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Fluctuations of Eigenvalues of a Polynomial on Haar Unitary and Finite Rank Matrices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月13日

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  • Benoît Collins,
  • Katsunori Fujie,
  • Takahiro Hasebe,
  • Felix Leid,
  • Noriyoshi Sakuma

摘要

This paper calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can give a complete algorithm for computing the fluctuations. When multiple eigenvalues are involved, we present several examples suggesting that a general algorithm would be much more complex.