LAUSR

Abstract We consider the moment space M 2 n + 1 d n of moments up to the order 2 n + 1 of d n × d n real matrix measures defined on the interval [ 0 , 1 ] . The asymptotic properties of the Hankel determinant { log det ( M i + j d n ) i , j = 0 , … , ⌊ n t ⌋ } t ∈ [ 0 , 1 ] of a uniformly distributed vector ( M 1 , … , M 2 n + 1 ) t ∼ U ( M 2 n + 1 ) are studied when the dimension n of the moment space and the size of the matrices d n 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.