Determinants of block Hankel matrices for random matrix-valued measures

Holger Dette and Dominik Tomecki

Stochastic Processes and their Applications, 2019, vol. 129, issue 12, 5200-5235

Abstract: We consider the moment space M2n+1dn of moments up to the order 2n+1 of dn×dn real matrix measures defined on the interval [0,1]. The asymptotic properties of the Hankel determinant {logdet(Mi+jdn)i,j=0,…,⌊nt⌋}t∈[0,1] of a uniformly distributed vector (M1,…,M2n+1)t∼U(M2n+1) are studied when the dimension n of the moment space and the size of the matrices dn converge to infinity. In particular weak convergence of an appropriately centered and standardized version of this process is established. Mod-Gaussian convergence is shown and several large and moderate deviation principles are derived. Our results are based on some new relations between determinants of subblocks of the Jacobi-beta-ensemble, which are of their own interest and generalize Bartlett decomposition-type results for the Jacobi-beta-ensemble from the literature.

Keywords: Mod-ϕ-convergence; Moment spaces; Matrix measures; Large deviations; Jacobi-beta-ensemble; Bartlett-decomposition (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.02.010

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