Complex determinantal processes and H1 noise

Details Complex determinantal processes and H1 noise Complex determinantal processes and H1 noise

2006-08-31

arxiv.org/abs/math/0608785v1

Electron. J. Probab. 12 (2007), no. 45, 1238-1257

Mathematics

Probability

22 pages, 1 figure

Scientific paper

For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinantal point processes with intensity rho dnu, where nu is the corresponding invariant measure. We show that as rho converges to infinity, after centering, these processes converge to invariant H1 noise. More precisely, for all functions f in the interesection of H1(nu) and L1(nu) the distribution of sum f(z) - rho/pi integral f dnu converges to Gaussian with mean 0 and variance given by ||f||_H1^2 / (4 pi).

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