Symmetric matrices, Catalan paths, and correlations
Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomial whose terms are the weights of domino tilings of a half Aztec diamond. They conjectured an analogue of this parametri...
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| Vydané v: | Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th... |
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| Hlavní autori: | , , |
| Médium: | Journal Article Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
DMTCS
22.04.2020
Discrete Mathematics & Theoretical Computer Science |
| Predmet: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almost-principal minors. Each entry is an explicit Laurent polynomial whose terms are the weights of domino tilings of a half Aztec diamond. They conjectured an analogue of this parametrization for symmetric matrices, where the Laurent monomials are indexed by Catalan paths. In this paper we prove the Kenyon-Pemantle conjecture, and apply this to a statistics problem pioneered by Joe (2006). Correlation matrices are represented by an explicit bijection from the cube to the elliptope. |
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| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.6337 |