Product Matrix Processes as Limits of Random Plane Partitions

Alexei Borodin, Vadim Gorin, Eugene Strahov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider a random process with discrete time formed by squared 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 squared 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.

Original languageAmerican English
Pages (from-to)6713-6768
Number of pages56
JournalInternational Mathematics Research Notices
Issue number20
StatePublished - 1 Oct 2020

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