Topologies of nodal sets of random band limited functions
Mathematical Physics
2014-11-25 v2 math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1312.7858,
title = {Topologies of nodal sets of random band limited functions},
author = {Peter Sarnak and Igor Wigman},
journal= {arXiv preprint arXiv:1312.7858},
year = {2014}
}
Comments
An announcement of recent results. Includes an announcement of the resolution of some open questions from the older version. 11 pages, 6 figures