A Matrix model for plane partitions

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.

Latex, 41 figures. Misprints and corrections. Changing the term TASEP to self avoiding particle porcess

References in corpus (3)

• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Universal distribution of random matrix eigenvalues near the "birth of a cut" transition