Interlacing adjacent levels of $\beta$-Jacobi corners processes

Vadim Gorin, Lingfu Zhang

We study the asymptotic of the global fluctuations for the difference between two adjacent level in the $\beta$--Jacobi corners process (multilevel and general $\beta$ extension of the classical Jacobi ensemble of random matrices). The limit is identified with the derivative of the $2d$ Gaussian Free Field. Our main tool is integral forms for the (Macdonald-type) difference operators originating from the Shuffle algebra.

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