A Matrix model for plane partitions

TL;DR

This paper introduces an exact matrix model for random plane partitions with arbitrary boundary conditions, enabling detailed analysis of their asymptotic behavior and universal regimes.

Contribution

It presents a novel exact matrix model for plane partitions, extending the analysis to arbitrary boundary conditions and large size asymptotics.

Findings

Exact large size asymptotic expansion of plane partitions

Description of universal regimes in plane partition models

Connection to TASEP-like processes with boundary conditions

Abstract

We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP-like process with arbitrary boundary conditions. Using the known solution of matrix models, this method allows to find the large size asymptotic expansion of plane partitions, to ALL orders. It also allows to describe several universal regimes.