Symmetric matrices, Catalan paths, and correlations
2020 ◽
Vol DMTCS Proceedings, 28th...
◽
Keyword(s):
International audience 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.
2012 ◽
Vol DMTCS Proceedings vol. AR,...
(Proceedings)
◽
Keyword(s):
2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
◽
2010 ◽
Vol DMTCS Proceedings vol. AN,...
(Proceedings)
◽
Keyword(s):
2018 ◽
Vol 341
(4)
◽
pp. 1185-1191
◽
1986 ◽
Vol 93
(6)
◽
pp. 462-464
◽
Keyword(s):
2011 ◽
Vol DMTCS Proceedings vol. AO,...
(Proceedings)
◽
Keyword(s):