Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (2): 937-956.doi: 10.1007/s10473-026-0221-3

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DEVIATION PROBABILITIES FOR SPECTRAL RADIUS OF PRODUCTS OF COMPLEX GINIBRE ENSEMBLES

Yutao MA*, Chaoyang SONG   

  1. School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China
  • Received:2024-09-06 Revised:2025-04-30 Published:2026-05-22
  • Contact: *Yutao MA, E-mail: mayt@bnu.edu.cn
  • About author:Chaoyang SONG, E-mail: songzhaoyang1209@126.com
  • Supported by:
    Ma's research was supported by the NSFC (12171038, 12571149) and the Key Research and Development Program of China (2020YFA0712900).

Abstract: Let $\boldsymbol{X}_1, \cdots, \boldsymbol{X}_{m_n}$ be independent $n\times n$ complex Ginibre ensembles and $Z_1, \cdots,$ $ Z_n$ be the eigenvalues of $\prod_{j=1}^{m_n} \boldsymbol{X}_j.$ Suppose $\lim\limits_{n\to\infty}m_n=+\infty,$ we obtain large and moderate deviations for $\max_{1\le i\le n} \log |Z_i|.$

Key words: products of complex Ginibre ensembles, spectral radius, large deviations, moderate deviations

CLC Number: 

  • 60G70
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