A note on 3d-monochromatic random waves and cancellation

2022/08/22 by Dalmao, Federico · 1 citation
#60D05 #60G15 #60G60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2208.10589

Abstract

In this note we prove that the asymptotic variance of the nodal length of complex-valued monochromatic random waves restricted to an increasing domain in \R³ 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.

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