The Elliptic Tail Kernel
Name
1907.11841.pdf
Description
Submitted version
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359.69 KB
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Adobe PDF
Checksum (MD5)
2b47b52fbf32020b48686da43354721e
Author(s)
Cuenca, Cesar
Gorin, Vadim
Olshanski, Grigori
Date Issued
2020
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Version
Original manuscript
Abstract
Abstract
We introduce and study a new family of $q$-translation-invariant determinantal point processes on the two-sided $q$-lattice. We prove that these processes are limits of the $q$–$zw$ measures, which arise in the $q$-deformation of harmonic analysis on $U(\infty )$, and express their correlation kernels in terms of Jacobi theta functions. As an application, we show that the $q$–$zw$ measures are diffuse. Our results also hint at a link between the two-sided $q$-lattice and rows/columns of Young diagrams.
We introduce and study a new family of $q$-translation-invariant determinantal point processes on the two-sided $q$-lattice. We prove that these processes are limits of the $q$–$zw$ measures, which arise in the $q$-deformation of harmonic analysis on $U(\infty )$, and express their correlation kernels in terms of Jacobi theta functions. As an application, we show that the $q$–$zw$ measures are diffuse. Our results also hint at a link between the two-sided $q$-lattice and rows/columns of Young diagrams.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNAA038
