Geometry of polynomials and applications

58 mins 48 secs, 813.29 MB, MPEG-4 Video 480x360, 25.0 fps, 44100 Hz, 1.84 Mbits/sec

About this item

Description:	Borcea, J (Stockholm) Wednesday 23 January 2008, 16:30-17:30 Zeros of Graph Polynomials

Created:

2008-02-03 18:15

Collection:

Combinatorics and Statistical Mechanics

Publisher:

Isaac Newton Institute

Borcea, J

Language:

eng (English)

Credits:

Author:

Borcea, J


Abstract:	We discuss closely related geometric properties of zero sets of multivariate polynomials such as real stability, the half-plane property, (Gårding) hyperbolicity and the strong Rayleigh property. In particular, using the latter we define a class of probability measures (called strongly Rayleigh) that contains uniform random spanning tree measures, determinantal measures (for contractions) and distributions for symmetric exclusion processes. We develop a theory of negative dependence for this class of measures and settle several conjectures of Liggett, Pemantle and Wagner. Examples and applications include extensions of Lyons' recent results on determinantal measures and the half-plane property for certain matroids studied by Sokal, Wagner et al. This is joint work with Petter Brändén (KTH) and Thomas M. Liggett (UCLA). Related Links * http://www.arxiv.org/abs/0707.2340 - PDF file of the paper on which the talk is based

Abstract:

We discuss closely related geometric properties of zero sets of multivariate polynomials such as real stability, the half-plane property, (Gårding) hyperbolicity and the strong Rayleigh property. In particular, using the latter we define a class of probability measures (called strongly Rayleigh) that contains uniform random spanning tree measures, determinantal measures (for contractions) and distributions for symmetric exclusion processes. We develop a theory of negative dependence for this class of measures and settle several conjectures of Liggett, Pemantle and Wagner. Examples and applications include extensions of Lyons' recent results on determinantal measures and the half-plane property for certain matroids studied by Sokal, Wagner et al.

This is joint work with Petter Brändén (KTH) and Thomas M. Liggett (UCLA).

Related Links
* http://www.arxiv.org/abs/0707.2340 - PDF file of the paper on which the talk is based

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