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arXiv · 1907.11841

The Elliptic Tail Kernel

Cesar Cuenca·Vadim Gorin·Grigori Olshanski
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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.

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BibTeXRIS

Cesar Cuenca, Vadim Gorin, Grigori Olshanski. 2019-07-27. The Elliptic Tail Kernel. https://doi.org/10.1093/imrn/rnaa038

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