Selecta Mathematica • Vol 30 • No 3
Tilted biorthogonal ensembles, Grothendieck random partitions, and determinantal tests
June 2024 • Svetlana Gavrilova, Leonid Petrov
Abstract We study probability measures on partitions based on symmetric Grothendieck polynomials. These deformations of Schur polynomials introduced in the K-theory of Grassmannians share many common properties. Our Grothendieck measures are analogs of the Schur measures on partitions introduced by Okounkov (Sel Math 7(1):57–81, 2001). Despite the similarity of determinantal formulas for the probability weights of Schur and Grothendieck measures, we demonstrate that Grothendieck measures are not determinantal poin…