Moment determinants as isomonodromic tau functions
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Bibliographic record
Abstract
] Centre de recherches mathématiques, Universite ́ de Montréal We consider a wide class of determinants whose entries are moments of the so-called semiclassical func-tionals and we show that they are tau functions for an appropriate isomonodromic family which depends on the parameters of the symbols for the functionals. This shows that the vanishing of the tau-function for those systems is the obstruction to the solvability of a Riemann–Hilbert problem associated to certain classes of (multiple) orthogonal polynomials. The determinants include Hänkel, Töplitz and shifted-Töplitz determinants as well as determinants of bimoment functionals and the determinants arising in the study of multiple orthogonality. Some of these determinants appear also as partition functions of random matrix models, including an instance of a two-matrix model.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
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| Bibliometrics | 0.000 | 0.000 |
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| Open science | 0.000 | 0.000 |
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| Insufficient payload (model declined to judge) | 0.008 | 0.009 |
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