The central limit problem for convex bodies
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- by Milla Anttila, Keith Ball and Irini Perissinaki
- Trans. Amer. Math. Soc. 355 (2003), 4723-4735
- DOI: https://doi.org/10.1090/S0002-9947-03-03085-X
- Published electronically: July 24, 2003
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Erratum: Trans. Amer. Math. Soc. 356 (2004), 2137-2137.
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
- Juan Arias-de-Reyna, Keith Ball, and Rafael Villa, Concentration of the distance in finite-dimensional normed spaces, Mathematika 45 (1998), no. 2, 245–252. MR 1695717, DOI 10.1112/S0025579300014182
- Keith Ball, An elementary introduction to modern convex geometry, Flavors of geometry, Math. Sci. Res. Inst. Publ., vol. 31, Cambridge Univ. Press, Cambridge, 1997, pp. 1–58. MR 1491097, DOI 10.2977/prims/1195164788
- Keith Ball, Logarithmically concave functions and sections of convex sets in $\textbf {R}^n$, Studia Math. 88 (1988), no. 1, 69–84. MR 932007, DOI 10.4064/sm-88-1-69-84
- Keith Ball and Irini Perissinaki, The subindependence of coordinate slabs in $l^n_p$ balls, Israel J. Math. 107 (1998), 289–299. MR 1658571, DOI 10.1007/BF02764013
- Persi Diaconis and David Freedman, Asymptotics of graphical projection pursuit, Ann. Statist. 12 (1984), no. 3, 793–815. MR 751274, DOI 10.1214/aos/1176346703
- M. Gromov and V. D. Milman, Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces, Compositio Math. 62 (1987), no. 3, 263–282. MR 901393
- László Lovász and Miklós Simonovits, The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume, 31st Annual Symposium on Foundations of Computer Science, Vol. I, II (St. Louis, MO, 1990) IEEE Comput. Soc. Press, Los Alamitos, CA, 1990, pp. 346–354. MR 1150706, DOI 10.1109/FSCS.1990.89553
- M. Meyer and S. Reisner, A geometric property of the boundary of symmetric convex bodies and convexity of flotation surfaces, Geom. Dedicata 37 (1991), no. 3, 327–337. MR 1094695, DOI 10.1007/BF00181409
- Gilles Pisier, The volume of convex bodies and Banach space geometry, Cambridge Tracts in Mathematics, vol. 94, Cambridge University Press, Cambridge, 1989. MR 1036275, DOI 10.1017/CBO9780511662454
- V. N. Sudakov, Typical distributions of linear functionals in finite-dimensional spaces of high dimension, Dokl. Akad. Nauk SSSR 243 (1978), no. 6, 1402–1405 (Russian). MR 517198
- Heinrich von Weizsäcker, Sudakov’s typical marginals, random linear functionals and a conditional central limit theorem, Probab. Theory Related Fields 107 (1997), no. 3, 313–324. MR 1440135, DOI 10.1007/s004400050087
Bibliographic 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
- MR Author ID: 232203
- Email: kmb@math.ucl.ac.uk
- Irini Perissinaki
- Affiliation: Department of Mathematics, University of Crete, 710409 Iraklion, Greece
- Email: irinip@math.uoc.gr
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1997580