Discrete and continuous Muttalib--Borodin processes: hard edge limit and large deviation principle
We consider a natural measure on plane partitions giving rise to a discrete-time Muttalib-Borodin process (MBP): each time-slice is a discrete version of a Muttalib-Borodin ensemble (MBE). The process is determinantal with explicit time-dependent correlation kernel. We study its hard-edge scaling limit, under appropriate scaling of the parameters, to obtain a discrete-time-dependent generalization of the classical continuous Bessel kernel of random matrix theory. The aforementioned hard edge limit gives rise to an extremal statistics distribution interpolating between the Tracy-Widom GUE and the Gumbel distributions. We discuss its interpretation in terms of directed last passage percolation (LPP) models. Finally, we derive the rate function for the large deviation priciple of the whole process. Based on joint works with D. Betea and with J. Husson and G. Mazzuca (in progress).
Area: IS22 - Universality, Stochastic PDEs and Random Growth (Giuseppe Cannizzaro)
Keywords: plane partitions, determinantal point process, last passage percolation
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