Laguerre entire functions and the Lee-Yang property

Laguerre entire functions are the polynomials of a single complex variable possessing real nonpositive zeros only or their limits on compact subsets of C. These functions are employed to establish a property of isotropic (i.e., OðNÞ-invariant) probability measures on R , N 2 N. It is called the Lee–Yang property since, in the case N 1⁄4 1, it corresponds to the property of the partition function of certain models of statistical physics, first established by T.D. Lee and C.N. Yang. A class of measures possessing this property is described. Certain connections of the Lee–Yang property with other aspects of the analytic theory of probability measures are discussed. 2002 Elsevier Science Inc. All rights reserved.