Small Scale CLTs for the Nodal Length of Monochromatic Waves

@article{Dierickx2022SmallSC,
  title={Small Scale CLTs for the Nodal Length of Monochromatic Waves},
  author={Gauthier Dierickx and Ivan Nourdin and Giovanni Peccati and Maurizia Rossi},
  journal={Communications in Mathematical Physics},
  year={2022}
}
We consider the nodal length $L(\lambda)$ of the restriction to a ball of radius $r_\lambda$ of a {\it Gaussian pullback monochromatic random wave} of parameter $\lambda>0$ associated with a Riemann surface $(\mathcal M,g)$ without conjugate points. Our main result is that, if $r_\lambda$ grows slower than $(\log \lambda)^{1/25}$, then (as $\lambda\to \infty$) the length $L(\lambda)$ verifies a Central Limit Theorem with the same scaling as Berry's random wave model -- as established in Nourdin… 

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