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Eigenvalue fluctuations of real valued centrosymmetric matrices

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  • Jana, Indrajit
  • Rani, Sunita

Abstract

We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence among them leads to behavior that differs from the classical CLT. The main contribution of this article is finding the expression of the variance of the limiting Gaussian distribution. The crux of the proof lies in combinatorial arguments that involve counting overlapping loops in complete undirected weighted graphs with growing degrees.

Suggested Citation

  • Jana, Indrajit & Rani, Sunita, 2026. "Eigenvalue fluctuations of real valued centrosymmetric matrices," Statistics & Probability Letters, Elsevier, vol. 237(C).
    • Handle: RePEc:eee:stapro:v:237:y:2026:i:c:s0167715226001689
    DOI: 10.1016/j.spl.2026.110804
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