Points on nodal lines with given direction

2018/02/26 by Rudnick, Zeev, Wigman, Igor
#11H99 #35P20 #60B99 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1802.09603

Abstract

We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.

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