DOAJ Open Access 2020

Symmetric matrices, Catalan paths, and correlations

Emmanuel Tsukerman Lauren Williams Bernd Sturmfels

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (3)

Emmanuel Tsukerman

Lauren Williams

Bernd Sturmfels

Format Sitasi

APA MLA BibTeX

Tsukerman, E., Williams, L., Sturmfels, B. (2020). Symmetric matrices, Catalan paths, and correlations. https://doi.org/10.46298/dmtcs.6337

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6337

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6337
Akses: Open Access ✓