@article{EJP446,
author = {Brian Rider and Balint Virag},
title = {Complex Determinantal Processes and $H1$ Noise},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {12},
year = {2007},
keywords = {determinantal process; random matrices; invariant point process; noise limit},
abstract = {For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinantal point processes $\mathcal Z_\rho$ with intensity $\rho d\nu$, where $\nu$ is the corresponding invariant measure. We show that as $\rho\to\infty$, after centering, these processes converge to invariant $H^1$ noise. More precisely, for all functions $f\in H^1(\nu) \cap L^1(\nu)$ the distribution of $\sum_{z\in \mathcal Z} f(z)-\frac{\rho}{\pi} \int f d \nu$ converges to Gaussian with mean zero and variance $ \frac{1}{4 \pi} \|f\|_{H^1}^2$.},
pages = {no. 45, 1238-1257},
issn = {1083-6489},
doi = {10.1214/EJP.v12-446},
url = {http://ejp.ejpecp.org/article/view/446}}