The talk will revolve around a probability distribution on plane partitions, which arises as a one-parameter generalization of the $q^{volume}$ measure in [Okounkov-Reshetikhin '03]. This generalization is closely related to the classical multivariate Hall-Littlewood polynomials, and it was first introduced in [Vuletic '09]. The main results describe the asymptotic behavior of the bottom slice of the plane partition under different limiting regimes. The emphasis of the talk will be on the use of (degenerations of) the Macdonald difference operators as a tool to obtain a class of observables and Fredholm-type formulas suitable for asymptotic analysis.

Evgeni Dimitrov (MIT)Fri, Feb 26

The talk will revolve around a probability distribution on plane partitions, which arises as a one-parameter generalization of the $q^{volume}$ measure in [Okounkov-Reshetikhin '03]. This generalization is closely related to the classical multivariate Hall-Littlewood polynomials, and it was first introduced in [Vuletic '09]. The main results describe the asymptotic behavior of the bottom slice of the plane partition under different limiting regimes. The emphasis of the talk will be on the use of (degenerations of) the Macdonald difference operators as a tool to obtain a class of observables and Fredholm-type formulas suitable for asymptotic analysis.