Hankel Determinants of Random Moment Sequences

For (t in [0,1]) let (underline{H}_{2lfloor nt rfloor } = (m_{i+j})_{i,j=0}^{lfloor nt rfloor }) denote the Hankel matrix of order (2lfloor nt rfloor ) of a random vector ((m_1,ldots ,m_{2n})) on the moment space (mathcal {M}_{2n}(I)) of all moments (up to the order 2n) of probability measures on the interval (I subset mathbb {R}). In this paper we study the asymptotic properties of the stochastic process ({ log det underline{H}_{2lfloor nt rfloor } }_{tin [0,1]}) as (n rightarrow infty ). In particular weak convergence and corresponding large deviation principles are derived after appropriate standardization.