The random plane wave is the centered stationary Gaussian process on the two dimensional plane whose spectral measure is the uniform measure on the unit circle. It is conjectured to be a universal object which captures the behaviour of high energy Laplace eigenfunctions on manifolds where the geodesic flow is ergodic. We study the number of connected components of its zero set on growing balls (centered at the origin), and show that it satisfies an exponential concentration result. This builds on the work of Nazarov-Sodin, who showed that there is a law of large number result for the component count.
This talk will be based on some parts of arXiv:2012.10302.
