Approximately gaussian marginals and the hyperplane conjecture
By Ronen Eldan, Bo'az Klartag. 2010
69 citations recorded by the source corpus.
We discuss connections between certain well-known open problems related to the uniform measure on a high-dimensional convex body. In particular, we show that the "thin shell conjecture" implies the "hyperplane conjecture". This extends a result by K. Ball, according to which the stronger "spectral gap conjecture" implies the "hyperplane conjecture".
Subfields: Applied Mathematics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/fcf960f20ea0dc630d3173c035ea3ca8f63f0fd7
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Emanuel Milman
- Van Hoang Nguyen
- Bo'az Klartag
- Christos Saroglou
- Franck Barthe
- Dario Cordero-Erausquin
- A. V. Kolesnikov
- Santosh Srinivas Vempala
In Molecular Biology
- Christos Saroglou
- Franck Barthe
- Dario Cordero-Erausquin
- Santosh Srinivas Vempala
- Benjamin R. Cousins
- Keith Ball
- Van Hoang Nguyen
- Bo'az Klartag
Citations in the corpus
- Invariances in variance estimates (2011, background): “This question is in fact related to the variance conjecture, as established in [14].”
- Bypassing KLS: Gaussian Cooling and an O^*(n3) Volume Algorithm (2014, methodology): “Indeed, it captures two well-known and much older conjectures from convex geometry, the slicing (or hyperplane) conjecture and the thin-shell conjecture (these were all shown to be equivalent in a certain sense recently [10, 11]), and thus has effectively evaded resolution for nearly a half-century.”
- Logarithmic bounds for isoperimetry and slices of convex sets (2023, methodology): “One could speculate that analysis of the H−1-norm of linear functionals, which played a crucial role in Klartag and Lehec [33], could help us understand this point.”
- Entropy jumps for isotropic log-concave random vectors and spectral gap (2012, background): “[18] B. Klartag, On convex perturbations with a bounded isotropic constant, Geom.”
- More on logarithmic sums of convex bodies (2014, background): “Surprisingly, it implies other major conjectures (see [11] [12]), such as the slicing problem and the KLS conjecture [24] up to a logarithmic factor.”