A matrix model for plane partitions

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 us to find the large size asymptotic expansion of plane partitions, to all orders. It also allows us to describe several universal regimes. On the algebraic geometry point of view, this gives the Gromov-Witten invariants of C(3) with branes, i.e. the topological vertex, in terms of the symplectic invariants of the mirror's spectral curve.