Palm measures for Dirac operators and the Sine beta process

TL;DR

This paper characterizes the Palm measure of the Sine beta process by relating it to the eigenvalues of a particular operator with boundary conditions, advancing understanding of this stochastic process.

Contribution

It introduces a novel characterization of the Palm measure for the Sine beta process through operator eigenvalues with boundary conditions.

Findings

Palm measure expressed via operator eigenvalues

Boundary conditions crucial for characterization

Enhanced understanding of Sine beta process

Abstract

We characterize the Palm measure of the Sine beta process as the eigenvalues of an associated operator with a specific boundary condition.