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The Lee-Yang and Polya-Schur Programs. II. Theory of Stable Polynomials and Applications
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1055-1474
2009 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 62, no 12, 1595-1631 p.Article in journal (Refereed) Published
Abstract [en]

In the first part of this series we characterized all linear operators on spaces of multivariate polynomials preserving the property of being nonvanishing in products of open circular domains. For such sets this completes the multivariate generalization of the classification program initiated by Polya and Schur for univariate real polynomials. We build on these classification theorems to develop here a theory of multivariate stable polynomials. Applications and examples show that this theory provides a natural framework for dealing in a uniform way with Lee-Yang type problems in statistical mechanics, combinatorics, and geometric function theory in one or several variables. In particular, we answer a question of Hinkkanen on multivariate apolarity.

Place, publisher, year, edition, pages
2009. Vol. 62, no 12, 1595-1631 p.
Keyword [en]
brownian intersection exponents, 1st-order phase-transitions, partition-function zeros, half-plane property, real zeros, multiplier, sequences, algebraic equations, invariant-theory, ferromagnets, systems
National Category
URN: urn:nbn:se:kth:diva-18909DOI: 10.1002/cpa.20295ISI: 000271299700001ScopusID: 2-s2.0-76749115349OAI: diva2:336956

QC 20100525

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2014-10-14Bibliographically approved

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Bränden, Petter
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