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The Limiting Characteristic Polynomial of Classical Random Matrix Ensembles

  • Reda Chhaibi
  • Emma Hovhannisyan
  • Joseph Najnudel
  • Ashkan Nikeghbali
  • Brad RodgersEmail author
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Abstract

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the Gaussian Unitary Ensemble. In fact, the result is the by-product of a general limit theorem for the convergence of random entire functions whose zeros present a simple regularity property.

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Notes

Acknowledgements

We would like to thank Elizabeth Meckes for an informative response regarding some of the bounds proved in Sect. 3, Sasha Sodin likewise for a helpful discussion, and an anonymous referee for several useful comments and corrections. B.R. was partially supported during this research by the NSF grant DMS-1701577.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Reda Chhaibi
    • 1
  • Emma Hovhannisyan
    • 2
  • Joseph Najnudel
    • 3
  • Ashkan Nikeghbali
    • 4
  • Brad Rodgers
    • 5
    Email author
  1. 1.ToulouseFrance
  2. 2.ZurichSwitzerland
  3. 3.BristolUK
  4. 4.ZurichSwitzerland
  5. 5.Kingston, ONCanada

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