Asymptotic shape of a random polytope in a convex body
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Publication:734344
DOI10.1016/j.jfa.2009.06.027zbMath1221.52009OpenAlexW2001147738MaRDI QIDQ734344
N. Dafnis, Apostolos Giannopoulos, Antonis Tsolomitis
Publication date: 20 October 2009
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2009.06.027
Random convex sets and integral geometry (aspects of convex geometry) (52A22) Asymptotic theory of convex bodies (52A23)
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Cites Work
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- \(L_{p}\)-moments of random vectors via majorizing measures
- Concentration of mass on convex bodies
- On singular values of matrices with independent rows
- Random vectors in the isotropic position
- A probabilistic approach to the geometry of the \(\ell^n_p\)-ball
- Random spaces generated by vertices of the cube
- Smallest singular value of random matrices and geometry of random polytopes
- Sampling convex bodies: a random matrix approach
- The Distribution of Rademacher Sums
- Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
- On the volume of caps and bounding the mean-width of an isotropic convex body
- Convex bodies, economic cap coverings, random polytopes
- Random walks and anO*(n5) volume algorithm for convex bodies
- Volume radius of a random polytope in a convex body
- Small ball probability estimates for log-concave measures
- Interpolation of Quasi-Normed Spaces.
- RANDOM POINTS IN ISOTROPIC UNCONDITIONAL CONVEX BODIES
- On the isotropic constant of random polytopes
- Concentration property on probability spaces.
