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On the Number of Nodal Domains of Random Spherical Harmonics

Fedor Nazarov and Mikhail Sodin
American Journal of Mathematics
Vol. 131, No. 5 (Oct., 2009), pp. 1337-1357
Stable URL: http://www.jstor.org/stable/40388552
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Number of Nodal Domains of Random Spherical Harmonics
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Abstract

Let N(f) be a number of nodal domains of a random Gaussian spherical harmonic f of degree n. We prove that as n grows to infinity, the mean of N(f)/n² tends to a positive constant a, and that N(f)/n² exponentially concentrates around a. This result is consistent with predictions made by Bogomolny and Schmit using a percolation-like model for nodal domains of random Gaussian plane waves.

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