# Gaussian fluctuations of Jack-deformed random Young diagrams

## TL;DR

This paper studies a new class of random Young diagrams deformed by Jack polynomials, demonstrating their convergence to a limit shape and Gaussian fluctuations around it.

## Contribution

It introduces a one-parameter deformation of classical Young diagram ensembles linked to Jack polynomials and analyzes their asymptotic behavior.

## Key findings

- Convergence of deformed Young diagrams to a limit shape
- Gaussian fluctuations around the limit shape
- Connection to Jack polynomials and characters

## Abstract

We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that each such a random Young diagram converges asymptotically to some limit shape and that the fluctuations around the limit are asymptotically Gaussian.