Quasi-invariance of fermion processes with J-Hermitian kernel

Abstract

Abstract. Fermion (or determinantal) processes with J-Hermitian kernel constitute a large class of random point fields which is of interest in mathematical physics. They generalize the popular family of fermion processes with Hermitian kernel and their existence has been recently established in full generality by Lytvynov [24]. In this paper we prove a quasi-invariance property for fermion processes with J-Hermitian kernel. Our findings extend in various directions the corresponding result in Camilier and Decreusefond [10].