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

Abstract

We study the asymptotics of the global fluctuations for the difference between two adjacent levels 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 tools are integral forms for the (Macdonald-type) difference operators originating from the shuffle algebra.