# Probabilistic aspects of the theory of vertex algebras

## TL;DR

This paper explores the use of vertex algebras to analyze determinantal processes on half-integer lines, establishing new connections with Virasoro operators and measures, and extending previous approaches to probabilistic models.

## Contribution

It introduces a novel link between z-measures and Virasoro algebra actions on Young diagrams, and defines Virasoro measures with proven determinancy.

## Key findings

- z-measures can be realized via Virasoro algebra actions
- Virasoro measures are shown to be determinantal
- Extension of vertex algebra methods to probabilistic processes

## 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.