Symmetric matrices, Catalan paths, and correlations
1 : Department of Mathematics, University of California, Berkeley, CA
2 : Berkeley University of California
(UC BERKELEY)

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University of California, Berkeley Department of Mathematics Berkeley, CA 94720, USA 
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Kenyon and Pemantle (2014) gave a formula for the entries of a square matrix in terms of connected principal and almostprincipal 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 KenyonPemantle 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.