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)/n 2 tends to a positive constant a, and that N(f)/n 2 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.
Original language | English |
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Pages (from-to) | 1337-1357 |
Number of pages | 21 |
Journal | American Journal of Mathematics |
Volume | 131 |
Issue number | 5 |
DOIs | |
State | Published - 2009 |