I will discuss a two-parameter family of probability measures, that are called ß-Krawtchouk corners processes. These measures are related to Jack symmetric functions, and can be thought of as integrable discretizations of ß- corners processes from random matrix theory, or alternatively as non-determinantal measures on lozenge tilings of infinite trapezoidal domains. For such models we show that the height function asymptotically concentrates around an explicit limit shape and prove that its limiting fluctuations are described by a pull-back of the Gaussian free field, which agrees with the one for Wigner matrices. If time permits, I will discuss the main tools we use to establish our results, which are certain multi-level loop equations. The talk is based on joint work with Alisa Knizel.
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