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The Elliptic Tail Kernel

Cuenca, Cesar and Gorin, Vadim and Olshanski, Grigori (2021) The Elliptic Tail Kernel. International Mathematics Research Notices, 2021 (19). pp. 14922-14964. ISSN 1073-7928. doi:10.1093/imrn/rnaa038.

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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.

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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 ( 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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Issue or Number:19
Record Number:CaltechAUTHORS:20220105-848738400
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Official Citation:Cesar Cuenca, Vadim Gorin, Grigori Olshanski, The Elliptic Tail Kernel, International Mathematics Research Notices, Volume 2021, Issue 19, October 2021, Pages 14922–14964,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112712
Deposited By: Tony Diaz
Deposited On:08 Jan 2022 21:59
Last Modified:09 Jan 2022 21:45

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