• Corpus ID: 251589443

Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder

  title={Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder},
  author={Massimo Notarnicola and Giovanni Peccati and Anna Vidotto},
We consider Berry’s random planar wave model (1977), and prove spatial functional limit theorems – in the high-energy limit – for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular domains. Our analysis is crucially based on a detailed study of the projection of nodal lengths onto the so-called second Wiener chaos , whose high-energy fluctuations are given by a Gaussian total disorder field indexed by polygonal curves. Such an exact… 
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