2004/07/01 by Fabrice Gamboa, Li-Vang Lozada-Chang · 1 citation
Mathematics · #Mathematical functions and polynomials #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math.PR #msc:30E05. #msc:60F10
paper · pdf · doi:10.1214/009117904000000559
published as Annals of Probability 2004, Vol. 32, No. 3B, 2819-2837 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000559
openalex publication_date 2004/07/01 · arxiv created 2004/10/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider the set Mn of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in Mn, we show that the upper canonical measure associated with this point satisfies a large deviation principle. Moderate deviation are also studied completing earlier results on asymptotic normality given by Chang, Kemperman and Studden [Ann. Probab. 21 (1993) 1295–1309]. Surprisingly, our large deviations results allow us to compute explicitly the (n+1)th moment range size of the set of all probability measures having the same n first moments. The main tool to obtain these results is the representation of Mn on canonical moments [see the book of Dette and Studden].