Small ball probability and Dvoretzky’s Theorem

By Bo'az Klartag, Roman Vershynin. 2004

59 citations recorded by the source corpus.

Large deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to small deviation results. In this note we present a novel application of a small deviations inequality to a problem that is related to the diameters of random sections of high dimensional convex bodies. Our results imply an unexpected distinction between the lower and upper inclusions in Dvoretzky’s Theorem.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0b06abd32d3b7c3de6843c14ed0e1c263b3aa302

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In Applied Mathematics

1. M. Soltanolkotabi
2. E.J. Candes
3. Grigoris Paouris
4. Roman Vershynin
5. Justin K. Romberg
6. David L. Donoho
7. Bo'az Klartag
8. Richard Baraniuk

In Geometry and Topology

1. E.J. Candes
2. Grigoris Paouris

Citations in the corpus

• A Geometric Analysis of Subspace Clustering with Outliers (2011, background): “According to [25], these appear in the first pages of [32].”
• Small ball probability estimates for log-concave measures (2012, methodology): “The same phenomenon occurs also for negative moments: we have the following theorem (see [15] and [14]): Theorem 5.”