Physics – Mathematical Physics
Scientific paper
2007-06-18
Physics
Mathematical Physics
20 pages
Scientific paper
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, and that N(f)/n^2 exponentially concentrates around that constant. This result is consistent with predictions made by Bogomolny and Schmit using a percolation-like model for nodal domains of random Gaussian plane waves.
Nazarov Fedor
Sodin Mikhail
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