The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912983179853824 |
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| author | Lazag, Pierre |
| author_facet | Lazag, Pierre |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_18141 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures Lazag, Pierre Mathematical Physics Combinatorics Probability 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. |
| title | The 2D Toda lattice hierarchy for multiplicative statistics of Schur measures |
| topic | Mathematical Physics Combinatorics Probability |
| url | https://arxiv.org/abs/2403.18141 |