• Corpus ID: 251589443

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

@inproceedings{Notarnicola2022FunctionalCO,
  title={Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder},
  author={Massimo Notarnicola and Giovanni Peccati and Anna Vidotto},
  year={2022}
}
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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References

SHOWING 1-10 OF 50 REFERENCES

Gaussian Random Measures Generated by Berry’s Nodal Sets

We consider vectors of random variables, obtained by restricting the length of the nodal set of Berry’s random wave model to a finite collection of (possibly overlapping) smooth compact subsets of

Non-Universality of Nodal Length Distribution for Arithmetic Random Waves

Abstract“Arithmetic random waves” are the Gaussian Laplace eigenfunctions on the two-dimensional torus (Rudnick and Wigman in Annales de l’Insitute Henri Poincaré 9(1):109–130, 2008; Krishnapur et

Fluctuations of the Nodal Length of Random Spherical Harmonics

Using the multiplicities of the Laplace eigenspace on the sphere (the space of spherical harmonics) we endow the space with Gaussian probability measure. This induces a notion of random Gaussian

Two point function for critical points of a random plane wave

Random plane wave is conjectured to be a universal model for high-energy eigenfunctions of the Laplace operator on generic compact Riemanian manifolds. This is known to be true on average. In the

Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature

For real (time-reversal symmetric) quantum billiards, the mean length L of nodal line is calculated for the nth mode (n>>1), with wavenumber k, using a Gaussian random wave model adapted locally to

Local Weak Limits of Laplace Eigenfunctions

In this paper, we introduce a new notion of convergence for the Laplace eigenfunctions in the semiclassical limit, the local weak convergence. This allows us to give a rigorous statement of Berry's

Phase singularities in complex arithmetic random waves

Complex arithmetic random waves are stationary Gaussian complex-valued solutions of the Helmholtz equation on the two-dimensional flat torus. We use Wiener-It\^o chaotic expansions in order to derive

Gaussian processes, kinematic formulae and Poincaré’s limit

We consider vector valued, unit variance Gaussian processes defined over stratified manifolds and the geometry of their excursion sets. In particular, we develop an explicit formula for the

Eigenfunctions and Random Waves in the Benjamini-Schramm limit

We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that Benjamini-Schramm convergence provides a unified language for the level and eigenvalue

On the area of excursion sets of spherical Gaussian eigenfunctions

The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivation arising from physics and