Discrete and Continuous Muttalib--Borodin process: Large deviations and Riemann--Hilbert analysis

Abstract: In this paper, we study the asymptotic behaviour of plane partitions distributed according to a weighted $q^{Volume}$ Muttalib--Borodin ensemble. Specifically, we establish a Large Deviation principle for the discrete Muttalib--Borodin process, characterising the rate function. Furthermore, through Riemann--Hilbert analysis, we give an explicit expression for the asymptotic shape of the partition.