Lee-Yang Problems and The Geometry of Multivariate Polynomials

Details Lee-Yang Problems and The Geometry of Multivariate Polynomials Lee-Yang Problems and The Geometry of Multivariate Polynomials

2008-10-06

arxiv.org/abs/0810.1007v1

Lett. Math. Phys. 86 (2008), 53-61

Mathematics

Complex Variables

To appear in Letters in Mathematical Physics; 8 pages, no figures, LaTeX2e

Scientific paper

10.1007/s11005-008-0271-6

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.

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