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Asymptotic behaviour of linear eigenvalue statistics of Hankel matrices

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  • A.S., Kiran Kumar
  • Maurya, Shambhu Nath

Abstract

We study linear eigenvalue statistics of band Hankel matrices with Brownian motion entries. We prove that the centred, normalized linear eigenvalue statistics of band Hankel matrices obey a central limit theorem (CLT) type result. We also discuss the convergence of linear eigenvalue statistics of band Hankel matrices with independent entries for odd power monomials. Our method is based on trace formula, moment method and some results of process convergence.

Suggested Citation

  • A.S., Kiran Kumar & Maurya, Shambhu Nath, 2022. "Asymptotic behaviour of linear eigenvalue statistics of Hankel matrices," Statistics & Probability Letters, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:stapro:v:181:y:2022:i:c:s0167715221002352
    DOI: 10.1016/j.spl.2021.109273
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    References listed on IDEAS

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    1. Maurya, Shambhu Nath & Saha, Koushik, 2020. "Process convergence of fluctuations of linear eigenvalue statistics of band Toeplitz matrices," Statistics & Probability Letters, Elsevier, vol. 166(C).
    2. Adhikari, Kartick & Saha, Koushik, 2018. "Universality in the fluctuation of eigenvalues of random circulant matrices," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 1-8.
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    1. Maurya, Shambhu Nath & Saha, Koushik, 2020. "Process convergence of fluctuations of linear eigenvalue statistics of band Toeplitz matrices," Statistics & Probability Letters, Elsevier, vol. 166(C).

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