Symmetric matrices, Catalan paths, and correlations - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2020

Symmetric matrices, Catalan paths, and correlations

Résumé

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.

Mots clés

Fichier principal
Vignette du fichier
document.pdf (8.57 Mo) Télécharger le fichier
Loading...

Dates et versions

hal-02166328 , version 1 (26-06-2019)

Identifiants

Citer

Emmanuel Tsukerman, Lauren Williams, Bernd Sturmfels. Symmetric matrices, Catalan paths, and correlations. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6337⟩. ⟨hal-02166328⟩
26 Consultations
410 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More