Topologies of Nodal Sets of Random Band-Limited Functions

Peter Sarnak; Igor Wigman

doi:10.1002/cpa.21794

Topologies of Nodal Sets of Random Band-Limited Functions

Peter Sarnak, Igor Wigman

Mathematics

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

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.

Original language	English (US)
Pages (from-to)	275-342
Number of pages	68
Journal	Communications on Pure and Applied Mathematics
Volume	72
Issue number	2
DOIs	https://doi.org/10.1002/cpa.21794
State	Published - Feb 1 2019

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1002/cpa.21794

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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.",

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AB - 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.

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Topologies of Nodal Sets of Random Band-Limited Functions

Abstract

All Science Journal Classification (ASJC) codes

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