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arXiv · 0810.1007

Lee-Yang Problems and The Geometry of Multivariate Polynomials

Julius Borcea·Petter Brändén
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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 Pólya-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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Julius Borcea, Petter Brändén. 2008-10-06. Lee-Yang Problems and The Geometry of Multivariate Polynomials. https://doi.org/10.1007/s11005-008-0271-6

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