Asymptotic behaviour of linear eigenvalue statistics of Hankel matrices

Kiran Kumar A.S. and Shambhu Nath Maurya

Statistics & Probability Letters, 2022, vol. 181, issue C

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.

Keywords: Linear eigenvalue statistics; Band Hankel matrix; Central limit theorem; Brownian motion; Time dependent fluctuations; Weak convergence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109273

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