Non-universality of the Nazarov-Sodin constant
  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. 
Par Kurlberg, Igor Wigman
math-ph math.MP