Volume Laws for Boxed Plane Partitions and Area Laws for Ferrers Diagrams

TL;DR

This paper investigates the asymptotic behavior of volume and area distributions in plane partitions and Ferrers diagrams, revealing mostly Gaussian limit laws across different symmetry classes and ensembles.

Contribution

It provides the first comprehensive asymptotic analysis of volume variables in symmetric and cyclically symmetric plane partitions and establishes area limit laws for Ferrers diagrams.

Findings

Most limit laws are Gaussian

Asymptotic analysis applies to various symmetry classes

Results include volume and area distribution laws

Abstract

We asymptotically analyse the volume-random variables of general, symmetric and cyclically symmetric plane partitions fitting inside a box. We consider the respective symmetry class equipped with the uniform distribution. We also prove area limit laws for two ensembles of Ferrers diagrams. Most of the limit laws are Gaussian.