Multivariate stable polynomials: theory and applications
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- by David G. Wagner PDF
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Abstract:
Univariate polynomials with only real roots, while special, do occur often enough that their properties can lead to interesting conclusions in diverse areas. Due mainly to the recent work of two young mathematicians, Julius Borcea and Petter Brändén, a very successful multivariate generalization of this method has been developed. The first part of this paper surveys some of the main results of this theory of multivariate stable polynomials—the most central of these results is the characterization of linear transformations preserving stability of polynomials. The second part presents various applications of this theory in complex analysis, matrix theory, probability and statistical mechanics, and combinatorics.References
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Additional Information
- David G. Wagner
- Affiliation: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- Email: dgwagner@math.uwaterloo.ca
- Received by editor(s): May 17, 2010
- Received by editor(s) in revised form: June 12, 2010
- Published electronically: October 4, 2010
- Additional Notes: Research supported by NSERC Discovery Grant OGP0105392.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Bull. Amer. Math. Soc. 48 (2011), 53-84
- MSC (2010): Primary 32A60; Secondary 05A20, 05B35, 15A45, 15A48, 60G55, 60K35
- DOI: https://doi.org/10.1090/S0273-0979-2010-01321-5
- MathSciNet review: 2738906
Dedicated: In memoriam of Julius Borcea