Probabilistic aspects of the theory of vertex algebras

Abstract

Determinantal processes on half-integer line can be studied using vertex algebras. They were used by Okounkov, where Schur processes were introduced and proved to be determinantal. We want to extend this vertex algebra approach. First, we establish the connection between the so-called z-measures and Virasoro operators. In fact, we prove that z-measures can be established by Virasoro algrebra action on Young diagrams space. Second, we introduce Virasoro measures and prove their determinancy.