A Note on Tail Triviality for Determinantal Point Processes

TL;DR

This paper provides a concise proof that determinantal point processes have a trivial tail sigma-field, confirming a conjecture previously proved by other researchers using different methods.

Contribution

It offers a new, short proof of the tail triviality for determinantal point processes, simplifying previous proofs and extending the discrete case result.

Findings

Determinantal point processes have a trivial tail sigma-field.

The paper confirms the conjecture using a shorter proof.

The proof extends the result from discrete to continuous cases.

Abstract

We give a very short proof that determinantal point processes have a trivial tail $\sigma$-field. This conjecture of the author has been proved by Osada and Osada as well as by Bufetov, Qiu, and Shamov. The former set of authors relied on the earlier result of the present author that the conjecture held in the discrete case, as does the present short proof.