The Elliptic Tail Kernel

Creators: Cuenca, Cesar; Gorin, Vadim; Olshanski, Grigori

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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