Grace-like polynomials
Ruelle, David
arXiv, 0009030 / Harvested from arXiv
Text on arXiv
Results of somewhat mysterious nature are known on the location of zeros of certain polynomials associated with statistical mechanics (Lee-Yang circle theorem) and also with graph counting. In an attempt at clarifying the situation we introduce and discuss here a natural class of polynomials. Let $P(z_1,...,z_m,w_1,...,w_n)$ be separately of degree 1 in each of its $m+n$ arguments. We say that $P$ is a Grace-like polynomial if $P(z_1,...,w_n)\ne0$ whenever there is a circle in ${\bf C}$ separating $z_1,...,z_m$ from $w_1,...,w_n$. A number of properties and characterizations of these polynomials are obtained.
Publié le : 2000-09-20
Classification:  Mathematical Physics 
@article{0009030,
     author = {Ruelle, David},
     title = {Grace-like polynomials},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0009030}
}

Ruelle, David. Grace-like polynomials. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0009030/