Central Limit Theorem on the Conjugacy Measure of Symmetric Groups

TL;DR

This paper establishes a central limit theorem for character ratios of random representations of symmetric groups using a new conjugacy measure derived from the conjugacy representation.

Contribution

It introduces a normalized conjugacy measure and proves a central limit theorem for character ratios, advancing understanding of symmetric group representations.

Findings

Proves a central limit theorem for character ratios

Defines a new conjugacy measure from the conjugacy representation

Provides insights into the distribution of characters in symmetric groups

Abstract

Regarding the conjugacy representation on symmetric groups, we initiate a normalized measure emerging from this representation, namely the conjugacy measure. A central limit theorem for character ratios of random representations of the symmetric group on the conjugacy measure is obtained.