Zmeasures on partitions and their scaling limits
Abstract
We study certain probability measures on partitions of n=1,2,..., originated in representation theory, and demonstrate their connections with random matrix theory and multivariate hypergeometric functions. Our measures depend on three parameters including an analog of the beta parameter in random matrix models. Under an appropriate limit transition as n goes to infinity, our measures converge to certain limit measures, which are of the same nature as onedimensional loggas with arbitrary beta>0. The first main result says that averages of products of ``characteristic polynomials'' with respect to the limit measures are given by the multivariate hypergeometric functions of type (2,0). The second main result is a computation of the limit correlation functions for the even values of beta.
 Publication:

arXiv eprints
 Pub Date:
 October 2002
 arXiv:
 arXiv:mathph/0210048
 Bibcode:
 2002math.ph..10048B
 Keywords:

 Mathematical Physics;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  Combinatorics;
 Mathematics  Mathematical Physics;
 Mathematics  Probability;
 Mathematics  Representation Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 AMSTeX, 37 pages