A note on $3d$-monochromatic random waves and cancellation

Federico Dalmao

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arXiv · 2208.10589

A note on $3d$-monochromatic random waves and cancellation

Federico Dalmao

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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 $\R^3$ 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.

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Federico Dalmao. 2022-08-22. A note on $3d$-monochromatic random waves and cancellation. https://arxiv.org/abs/2208.10589

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