Abstract
We discuss several examples of point processes [all taken from Hough et al. (Zeros of Gaussian analytic functions and determinantal point processes, 2009)] for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and permanental point processes, as well as an isometry-invariant point process that arises as the zero set of a Gaussian random analytic function.
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Acknowledgments
We thank Manjunath Krishnapur for drawing our attention to Gaussian analytic functions. We also thank the reviewers for their useful comments. This project was supported by the German Research Foundation (DFG), within the CRC 701. Robert V. Moody was also supported by the Natural Sciences and Engineering Research Council of Canada.
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Baake, M., Kösters, H. & Moody, R.V. Diffraction Theory of Point Processes: Systems with Clumping and Repulsion. J Stat Phys 159, 915–936 (2015). https://doi.org/10.1007/s10955-014-1178-5
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DOI: https://doi.org/10.1007/s10955-014-1178-5