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Creators/Authors contains: "Olshanski, Grigori"

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  1. ; ; (, International Mathematics Research Notices)
    null (Ed.)
    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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