Complex determinantal processes and H1 noise
Brian Rider, University of Colorado, Boulder
Balint Virag, University of Toronto
Abstract
For the plane, sphere, and hyperbolic plane we
consider the canonical invariant determinantal point
processes with intensity ρ dν, where ν is the
corresponding invariant measure. We show that as ρ
converges to infinity, after centering, these processes
converge to invariant H1 noise. More precisely, for all
functions f in the intersection of H1(ν) and L1(ν) the
distribution of ∑ f(z) - ρ/π ∫ f dν converges
to Gaussian with mean 0 and variance given by ||f||_H1^2/
(4 π).
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