Product Matrix Processes as Limits of Random Plane Partitions. (16th January 2019)

• Record Type: Journal Article
• Authors: Borodin, Alexei; Gorin, Vadim; Strahov, Eugene
• Is Part Of: International mathematics research notices. Volume 2020:Number 20(2020)
• Page Start: 6713
• Page End: 6768
• Publication Date: 2019-01-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rny297
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: 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.