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 Electronic Journal of Probability > Vol. 12 (2007) > Paper 45 open journal systems 


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).


Full text: PDF

Pages: 1238-1257

Published on: October 9, 2007
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Electronic Journal of Probability. ISSN: 1083-6489