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arXiv · 2403.18141

The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures

Pierre Lazag
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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.

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Pierre Lazag. 2024-03-26. The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures. https://arxiv.org/abs/2403.18141

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