Lee-Yang Problems and The Geometry of Multivariate Polynomials
Complex Variables
2008-11-17 v1 Statistical Mechanics
Mathematical Physics
Combinatorics
math.MP
Abstract
We describe all linear operators on spaces of multivariate polynomials preserving the property of being non-vanishing in open circular domains. This completes the multivariate generalization of the classification program initiated by P\'olya-Schur for univariate real polynomials and provides a natural framework for dealing in a uniform way with Lee-Yang type problems in statistical mechanics, combinatorics, and geometric function theory. This is an announcement with some of the main results in arXiv:0809.0401 and arXiv:0809.3087.
Keywords
Cite
@article{arxiv.0810.1007,
title = {Lee-Yang Problems and The Geometry of Multivariate Polynomials},
author = {Julius Borcea and Petter Brändén},
journal= {arXiv preprint arXiv:0810.1007},
year = {2008}
}
Comments
To appear in Letters in Mathematical Physics; 8 pages, no figures, LaTeX2e