Topologies of nodal sets of random band limited functions

Abstract

It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the supports of these distributions are determined. In particular the results apply to random monochromatic waves and to random real algebraic hyper-surfaces in projective space.

arXiv commentAn announcement of recent results. Includes an announcement of the resolution of some open questions from the older version. 11 pages, 6 figures