On complex Lee and Yang polynomials (Q679350)

The author studies a class of complex polynomials in many variables \(P_n(z_1,\dots,z_n)\) which has the property that all the roots of the univariate polynomial \(P_n(z,\dots,z)\) are inside the unit circle. These polynomials are relevant to statistical mechanics [see \textit{D. Ruelle}, Statistical mechanics. Rigorous results, New York, Benjamin (1969; Zbl 0177.57301)]. The proof is based on conformal transforms and on `decoupling procedures'. The author also studies a family of inner functions in several complex variables associated to the complex Lee and Yang polynomials.