Random vectors with the Lee–Yang property

Notion of the “Lee–Yang property” is introduced on the basis of the analysis of various applications of the Lee–Yang theorem to isotropic distributions of random vectors in statistical physics and quantum field theory. A class of probability distributions enjoying this property is constructed which includes the well-known $P(\varphi)$ models of quantum field theory. A number of new inequalities is established for vectors enjoying; the Lee–Yang property.