A note on 3d-monochromatic random waves and cancellation

Abstract

In this note we prove that the asymptotic variance of the nodal length of complexvalued monochromatic random waves restricted to an increasing domain in R 3 is linear in the volume of the domain.Put together with previous results this shows that a Central Limit Theorem holds true for 3-dimensional monochromatic random waves.We compare with the variance of the nodal length of the real-valued 2-dimensional monochromatic random waves where a faster divergence rate is observed, this fact is connected with Berry's cancellation phenomenon.Moreover, we show that a concentration phenomenon takes place.

Locations

• Latin American Journal of Probability and Mathematical Statistics - View
• arXiv (Cornell University) - View - PDF