Filament structure of random waves

Abstract We investigate the small-scale equidistribution properties of random waves, u , in R n . Numerical evidence suggests that such objects display a fine scale filament structure. show x-ray $|u|^{2}$?> | u 2 along any line segment is uniformly equidistributed. So limiting behaviour must be weaker than L 2 scarring. On other hand, we at Planck phase space there are (with high probability) logarithmic fluctuations above what would expected given equidistribution. Taken together these results suggest structure may configuration echo phase-space concentrations.