English

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 0<q10<q\leq 1. Consequences are proofs of the strongest conjecture of Mason and negative dependence properties for qq-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

R2 v1 2026-06-23T05:04:19.584Z