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The central limit problem for convex bodies
Author(s):
Milla
Anttila;
Keith
Ball;
Irini
Perissinaki
Journal:
Trans. Amer. Math. Soc.
355
(2003),
4723-4735.
MSC (2000):
Primary 52A22;
Secondary 60F05
Posted:
July 24, 2003
Errata:
Trans. Amer. Math. Soc. 356 (2004), 2137.
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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.
References:
-
- 1.
- J.Arias de Reyna, K.Ball and R.Villa: Concentration of the distance in finite-dimensional normed spaces, Mathematika 45, 245-252, 1998. MR 2000b:46013
- 2.
- K.Ball: An Elementary Introduction to Modern Convex Geometry, Flavors of Geometry, Mathematical Sciences Research Institute Publications 31, Cambridge Univ. Press, 1997, pp. 1-58. MR 99f:52002
- 3.
- K.Ball: Logarithmically concave functions and sections of convex sets in
 , Stud. Math. 88, No.1, 69-84, 1988. MR 89e:52002 - 4.
- K.Ball and I.Perissinaki: Subindependence of coordinate slabs in
 balls, Israel J. Math. 107, 289-299, 1998. MR 99k:52012 - 5.
- P.Diaconis and D.Freedman: Asymptotics of graphical projection pursuit, Ann. of Stat. 12, 793-815, 1984. MR 86b:62011
- 6.
- M. Gromov and V. Milman: Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces, Compos. Math. 62, 263-282, 1987. MR 89f:46031
- 7.
- L.Lovász and M.Simonovits: Mixing rate of Markov chains, an isoperimetric inequality, and computing the volume, Proc. 31st Annual Symp. on Found. of Computer Science, IEEE Computer Soc., 346-355, 1990. MR 93e:68035
- 8.
- M.Meyer and S.Reisner: A geometric property of the boundary of symmetric convex bodies and convexity of flotation surfaces, Geom Dedicata 37, No 3, 327-337, 1991 MR 92a:52003
- 9.
- G. Pisier: The volume of convex bodies and Banach space geometry, Tracts in Math. 94, Cambridge Univ. Press, 1989. MR 91d:52005
- 10.
- V. Sudakov: Typical distributions of linear functionals in finite-dimensional spaces of high dimension, Soviet Math. Dokl. 19 No 6, 1578-1582, 1978 MR 80b:60011
- 11.
- H.von Weizsäcker: Sudakov's typical marginals, random linear functionals and a conditional central limit theorem, Probab. Theory Relat. Fields 107, 313-324, 1997. MR 99c:60006
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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:
10.1090/S0002-9947-03-03085-X
PII:
S 0002-9947(03)03085-X
Received by editor(s):
July 14, 1999
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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