Product Matrix Processes as Limits of Random Plane Partitions
Name
1806.10855.pdf
Description
Submitted version
Size
686.34 KB
Format
Adobe PDF
Checksum (MD5)
f5897de4ec887c4fadfbc000f80488e0
Author(s)
Borodin, Alexei
Gorin, Vadim
Strahov, Eugene
Date Issued
January 2019
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Citation
Borodin, Alexei, et al. "Product Matrix Processes as Limits of Random Plane Partitions." International Mathematics Research Notices (January 2019) © The Author(s) 2019
Version
Original manuscript
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. Keywords: products of random matrices; multi-level determinantal point processes; Schur processes; random plane partitions
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://dx.doi.org/10.1103/10.1093/IMRN/RNY297
