On some particular Muttalib--Borodin ensembles and their hard edge scaling limit

by Dan Betea (KU Leuven)

Location: BBB online, Leuven
Time: Tuesday June 23, 2020 at 15:00

We introduce a simple probability measure on plane partitions (lozenge tilings) leading to correlated \(q\)-discrete Muttalib–Borodin ensembles (MBEs) where in some sense both Vandermonde interactions come with their own exponents. Marginals of this measure contain, as degenerate cases, Johansson’s Meixner ensemble from last passage percolation and the little \(q\)-Jacobi ensemble of plane partitions. In the finite \(N\) (Heckman–Opdam-like) continuous limit we obtain a mild generalization of Borodin’s Jacobi-like Muttalib ensemble—properly, a process of correlated such ensembles. We scale the later in the hard edge limit—around zero—to obtain a determinantal point process with kernel given in terms of the Fox H-function https://en.wikipedia.org/wiki/Fox_H-function . This work is motivated by recent results of Molag and Kuijlaars, as well as Claeys, on MBEs and their scaling limits.