Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces

TL;DR

This paper demonstrates that determinantal point processes linked to de Branges spaces are rigid and, under certain conditions, quasi-invariant under compactly supported diffeomorphisms, revealing new structural properties of these processes.

Contribution

It establishes rigidity and quasi-invariance properties for determinantal point processes associated with de Branges spaces, extending understanding of their symmetries and stability.

Findings

Determinantal point processes are rigid on the real line.

Under certain assumptions, these processes are quasi-invariant under compactly supported diffeomorphisms.

The results connect de Branges spaces with structural properties of associated point processes.

Abstract

In this note, we show that determinantal point processes on the real line corresponding to de Branges spaces of entire functions are rigid in the sense of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under the group of diffeomorphisms of the line with compact support.