Two point function for critical points of a random plane wave

Author: 

Beliaev, D
Cammarota, V
Wigman, I

Publication Date: 

31 August 2017

Journal: 

International Mathematics Research Notices

Last Updated: 

2020-08-14T14:47:25.91+01:00

Issue: 

9

Volume: 

2019

DOI: 

10.1093/imrn/rnx197

page: 

2661–2689-

abstract: 

Random plane wave is conjectured to be a universal model for high-energy eigenfunctions of the Laplace operator on generic compact Riemannian manifolds. This is known to be true on average. In the present paper we discuss one of important geometric observable: critical points. We first compute one-point function for the critical point process, in particular we compute the expected number of critical points inside any open set. After that we compute the short-range asymptotic behaviour of the two-point function. This gives an unexpected result that the second factorial moment of the number of critical points in a small disc scales as the fourth power of the radius.

Symplectic id: 

724603

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article