CENTRAL LIMIT THEOREM FOR PLANCK-SCALE MASS DISTRIBUTION OF TORAL LAPLACE EIGENFUNCTIONS

Igor Wigman, Nadav Yesha

Research output: Contribution to journalArticlepeer-review

Abstract

We study the fine-scale (Formula presented.) -mass distribution of toral Laplace eigenfunctions with respect to random position in two and three dimensions. In two dimensions, under certain flatness assumptions on the Fourier coefficients and generic restrictions on energy levels, both the asymptotic shape of the variance is determined and the limiting Gaussian law is established in the optimal Planck-scale regime. In three dimensions the asymptotic behaviour of the variance is analysed in a more restrictive scenario (“Bourgain's eigenfunctions”). Other than the said precise results, lower and upper bounds are proved for the variance under more general flatness assumptions on the Fourier coefficients.

Original languageEnglish
Pages (from-to)643-676
Number of pages34
JournalMathematika
Volume65
Issue number3
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 University College London

Keywords

  • 11H06
  • 11Z05
  • 35P20 (primary)

ASJC Scopus subject areas

  • General Mathematics

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