On the approximate normality of eigenfunctions of the Laplacian

Author:
Elizabeth Meckes

Journal:
Trans. Amer. Math. Soc. **361** (2009), 5377-5399

MSC (2000):
Primary 58J50; Secondary 60F05, 58J65

Published electronically:
May 4, 2009

MathSciNet review:
2515815

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result of this paper is a bound on the distance between the distribution of an eigenfunction of the Laplacian on a compact Riemannian manifold and the Gaussian distribution. If is a random point on a manifold and is an eigenfunction of the Laplacian with -norm one and eigenvalue , then

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Additional Information

**Elizabeth Meckes**

Affiliation:
Department of Mathematics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44122

Email:
elizabeth.meckes@case.edu

DOI:
https://doi.org/10.1090/S0002-9947-09-04661-3

Keywords:
Eigenfunctions,
Laplacian,
value distributions,
spherical harmonics,
random waves,
Stein's method,
normal approximation

Received by editor(s):
May 17, 2007

Received by editor(s) in revised form:
October 9, 2007

Published electronically:
May 4, 2009

Additional Notes:
This research was supported by fellowships from the ARCS Foundation and the American Institute of Mathematics.

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.