CaltechAUTHORS
Published October 2021 | Version Submitted
Journal Article Open

The Elliptic Tail Kernel

Creators

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon University of Wisconsin–Madison
  • 3. ROR icon Massachusetts Institute of Technology
  • 4. ROR icon Institute for Information Transmission Problems
  • 5. ROR icon Skolkovo Institute of Science and Technology
  • 6. ROR icon National Research University Higher School of Economics

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(∞)⁠, 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.

Additional Information

© The Author(s) 2020. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). Received September 16, 2019; Revised January 31, 2020; Accepted February 6, 2020. Published: 03 March 2020. The authors would like to thank the anonymous referee for bringing [34] to our attention. Communicated by Prof. Alexei Borodin. This work was supported by the National Science Foundation grant [DMS-1664619 to C.C. and V.G.]; NEC Corporation Fund for Research in Computers and Communications [to V.G.] and National Science Foundation grant [DMS-1949820 to V.G.].

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Additional details

Identifiers

Eprint ID
112712
DOI
10.1093/imrn/rnaa038
Resolver ID
CaltechAUTHORS:20220105-848738400

Related works

Describes
10.1093/imrn/rnaa038 (DOI)
https://arxiv.org/abs/1907.11841 (URL)

Funding

NSF
DMS-1664619
NEC Corporation
NSF
DMS-1949820

Dates

Created
2022-01-08
Created from EPrint's datestamp field
Updated
2022-01-09
Created from EPrint's last_modified field