A central limit theorem for projections of the cube

We prove a central limit theorem for the volume of projections of the cube [ - 1 , 1 ] N onto a random subspace of dimension n , when n is fixed and N → ∞ . Randomness in this case is with respect to the Haar measure on the Grassmannian manifold.

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Bibliographic Details
Published inProbability theory and related fields Vol. 159; no. 3-4; pp. 701 - 719
Main Authors Paouris, Grigoris, Pivovarov, Peter, Zinn, Joel
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014
Springer Nature B.V
Subjects
Central limit theorem
Cubes
Economics
Finance
Geometry
Insurance
Management
Manifolds
Manifolds (mathematics)
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability theory
Probability Theory and Stochastic Processes
Projection
Quantitative Finance
Random variables
Randomness
Statistics for Business
Studies
Subspaces
Texts
Theorems
Theoretical
Topological manifolds
60D05 (Geometric probability and stochastic geometry)
60F05 (Central limit and other weak theorems)
Primary 52A23 (Asymptotic theory of convex bodies)
Secondary 52A22 (Random convex sets and integral geometry)
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Summary:We prove a central limit theorem for the volume of projections of the cube [ - 1 , 1 ] N onto a random subspace of dimension n , when n is fixed and N → ∞ . Randomness in this case is with respect to the Haar measure on the Grassmannian manifold.
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ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-013-0518-8