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.
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