The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures
Mathematical Physics
2026-03-27 v3 Combinatorics
math.MP
Probability
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 \cite{okounkovschurmeasures} and of Cafasso-Ruzza in \cite{cafassoruzza} concerning the finite-temperature Plancherel measure. Our proof lies on the semi-infinite wedge formalism and the Boson-Fermion correspondance.
Keywords
Cite
@article{arxiv.2403.18141,
title = {The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures},
author = {Pierre Lazag},
journal= {arXiv preprint arXiv:2403.18141},
year = {2026}
}