Abstract
We investigate the number of nodal intersections of ran- dom Gaussian Laplace eigenfunctions on the standard three-dimensional at torus with a xed smooth reference curve, which has nowhere vanishing curvature. The expected intersection number is universally proportional to the length of the reference curve, times the wavenum- ber, independent of the geometry. Our main result gives a bound for the variance, if either the torsion of the curve is nowhere zero or if the curve is planar.
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