Hodge-Riemann relations for Potts model partition functions
Combinatorics
2019-02-12 v2 Probability
Abstract
We prove that the Hessians of nonzero partial derivatives of the (homogenous) multivariate Tutte polynomial of any matroid have exactly one positive eigenvalue on the positive orthant when . Consequences are proofs of the strongest conjecture of Mason and negative dependence properties for -state Potts model partition functions.
Cite
@article{arxiv.1811.01696,
title = {Hodge-Riemann relations for Potts model partition functions},
author = {Petter Brändén and June Huh},
journal= {arXiv preprint arXiv:1811.01696},
year = {2019}
}
Comments
7 pages