Partial sum of matrix entries of representations of the symmetric group and its asymptotics

Dario De Stavola

Published 2016-06-29Version 1

Many aspects of the asymptotics of Plancherel distributed partitions have been studied in the past fifty years, in particular the limit shape, the distribution of the longest rows, characters of the associated representation matrices of the symmetric group, and connections with random matrix theory. The latter prompts us to study the representation matrices themselves. We consider thus partial sums of entries of the representation matrix. These partial sums have a natural decomposition as a main term and a remainder. In this paper we describe the fluctuations of the main term. Our main tool is the expansion of symmetric functions evaluated on Jucys-Murphy elements.