Decay of Correlations for Multiplicative Functionals of Determinantal Point Processes

Abstract

The main result of this paper is an upper bound on the correlations of multiplicative functionals of determinantal point processes. In particular, for the sine process, the correlations of a multiplicative functional associated with a rapidly decaying function decay quadratically. It follows that the spectral density of such functionals belongs to the Sobolev space $H_1$.