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September 18, 2025NonlinearityOpen Access

Universality for random matrices with an edge spectrum singularity

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Authors

TBThomas BothnerUniversity of BristolTSTheodore G. ShepherdForschungszentrum Jülich

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Implication

This analysis reveals singular behavior in random matrices, highlighting implications for density of states and orthogonal polynomials.

Key Points

  • This study uncovers singular behaviors in random matrices around edge spectra, contributing to the understanding of density of states.
  • Key evidence showcases results extending previous findings with Riemann-Hilbert problems, enhancing insights about singularity effects.
  • Using complex Hermitian matrices, we address the asymptotic behavior of invariant random matrix ensembles at large dimensions.
  • Findings underscore the importance of Painlevé-XXXIV solutions, suggesting deeper connections in integrable systems.

Cite This Study

Bothner et al. (2025) studied this question.

synapsesocial.com/papers/68d461cb31b076d99fa61424https://doi.org/10.1088/1361-6544/ae0401
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Also Consider

Synapse has enriched 3 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation1993 · 1,447 citations
  2. 2Painlevé XXXIV Asymptotics of Orthogonal Polynomials for the Gaussian Weight with a Jump at the Edge2011 · 36 citations
  3. 3Critical Edge Behavior in Unitary Random Matrix Ensembles and the Thirty-Fourth Painlevé Transcendent2008 · 59 citations