The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures
Abstract
We prove Fredholm determinants build out from generalizations of Schur measures, or equivalently, arbitrary multiplicative statistics of the original Schur measures are tau-functions of the 2D Toda lattice hierarchy. Our result apply to finite temperature Schur measures, and extends both the result of Okounkov in okounkovschurmeasures and of Cafasso-Ruzza in cafassoruzza concerning the finite-temperature Plancherel measure. Our proof lies on the semi-infinite wedge formalism and the Boson-Fermion correspondance.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.