Hankel determinants of random moment sequences

Abstract

For $t\in [0,1]$ let ${\underline{H}}_{2\lfloor nt\rfloor }=(m_{i+j}{)}_{i,j=0}^{\lfloor nt\rfloor }$ denote the Hankel matrix of order $2\lfloor nt\rfloor$ of a random vector $(m_1,\dots ,m_{2n})$ 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 $\{\log \det {\underline{H}}_{2\lfloor nt\rfloor }{\}}_{t\in [0,1]}$ as $n\to \infty$. In particular weak convergence and corresponding large deviation principles are derived after appropriate standardization.

Keyword and Phrases: Hankel determinant, random moment sequences, weak convergence, large deviation principle, canonical moments, arcsine distribution AMS Subject Classification: 60F05, 60F10, 30E05, 15B52

References in corpus (1)

• The smallest eigenvalue of Hankel matrices