Year: 2020
Type: article
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.
DOI: 10.1093/imrn/rnaa038
Authors: Cesar Cuenca, Vadim Gorin, Grigori Olshanski
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W2966402841