The Elliptic Tail Kernel. (3rd March 2020)

• Record Type: Journal Article
• Authors: Cuenca, Cesar; Gorin, Vadim; Olshanski, Grigori
• Is Part Of: International mathematics research notices. Volume 2021:Number 19(2021)
• Page Start: 14922
• Page End: 14964
• Publication Date: 2020-03-03
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnaa038
• Languages: English
• ISSNs: 1073-7928

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.