# Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves

This is joint work with Par Kurlberg.
We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for “arithmetic random waves”, i.e. random toral Laplace eigenfunctions.