The central limit problem for convex bodies

Authors:
Milla Anttila, Keith Ball and Irini Perissinaki

Journal:
Trans. Amer. Math. Soc. **355** (2003), 4723-4735

MSC (2000):
Primary 52A22; Secondary 60F05

DOI:
https://doi.org/10.1090/S0002-9947-03-03085-X

Published electronically:
July 24, 2003

Erratum:
Trans. Amer. Math. Soc. 356 (2004), 2137.

MathSciNet review:
1997580

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that every symmetric convex body which satisfies a kind of weak law of large numbers has the property that almost all its marginal distributions are approximately Gaussian. Several quite broad classes of bodies are shown to satisfy the condition.

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Additional Information

**Milla Anttila**

Affiliation:
Department of Mathematics, University of Kuopio, pl 1627, 70211 Kuopio, Finland

Email:
meanttila@hytti.uku.fi

**Keith Ball**

Affiliation:
Department of Mathematics, University College, University of London, Gower Street, London WC1E 6BT, England

Email:
kmb@math.ucl.ac.uk

**Irini Perissinaki**

Affiliation:
Department of Mathematics, University of Crete, 710409 Iraklion, Greece

Email:
irinip@math.uoc.gr

DOI:
https://doi.org/10.1090/S0002-9947-03-03085-X

Received by editor(s):
July 14, 1999

Published electronically:
July 24, 2003

Additional Notes:
The first author was supported by EPSRC-97409672, and the second author was supported in part by NSF grant DMS-9257020

Article copyright:
© Copyright 2003
American Mathematical Society