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

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.

9 pages, 1 figure, published in proceedings of the Fifth Colloquium on Mathematics and Computer Science