A Matrix model for plane partitions

Bertrand Eynard (1)

1 SPhT - Service de Physique Théorique

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.

Mots clés: partitions; random matrices; matrix model; tasep

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Bertrand Eynard. A Matrix model for plane partitions. 2009. ⟨hal-00381019v3⟩