3 years ago

Topologies of Nodal Sets of Random Band‐Limited Functions

Peter Sarnak, Igor Wigman

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 hypersurfaces in projective space.© 2018 Wiley Periodicals, Inc.

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