Product matrix processes as limits of random plane partitions
Mathematical Physics
2020-07-24 v1 Combinatorics
math.MP
Abstract
We consider a random process with discrete time formed by singular values of products of truncations of Haar distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives determinantal formulas for (dynamical) correlation functions and a contour integral representation for the correlation kernel. The relation with the Schur processes implies that the continuous limit of marginals for q-distributed plane partitions coincides with the joint law of singular values for products of truncations of Haar-distributed random unitary matrices. We provide structural reasons for this coincidence that may also extend to other classes of random matrices.
Cite
@article{arxiv.1806.10855,
title = {Product matrix processes as limits of random plane partitions},
author = {Alexei Borodin and Vadim Gorin and Eugene Strahov},
journal= {arXiv preprint arXiv:1806.10855},
year = {2020}
}