On convex perturbations with a bounded isotropic constant

By Bo'az Klartag. 2006

274 citations recorded by the source corpus.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/e86e750a29c3eccb630f05f14574cf63ab704b23

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In Applied Mathematics

In Molecular Biology

Citations in the corpus

Small ball probability estimates for log-concave measures (2012, background): “The best known bound is due to B. Klartag: f(0)1=n 6 Cn1=4 (see [ 11 ]).”
Approximately gaussian marginals and the hyperplane conjecture (2010, background): “Begin by recalling the technique from [16].”
Rogers–Shephard inequality for log-concave functions (2014, background): “The far reaching influence of this inequality becomes evident as it can be found as an ingredient not only in many important works in classical and asymptotic convex geometry [11,23,21,26] but also in many others with a”
More on logarithmic sums of convex bodies (2014, background): “The best estimate up to date for the upper bound is of the order n1/4, due to Klartag [25] after improving the previous estimate Cn1/4 log n by Bourgain [7].”
Relative entropy of cone measures and Lp centroid bodies (2009, background): “We make use of the following lemma due to Klartag [24] (Lemmas 4.3 and 4.5).”
On the hyperplane conjecture for random convex sets (2006, background): “We refer the reader to, e.g., [2], [18] or [ 14 ] for partial results, history and for additional literature regarding this hyperplane conjecture.”
Concentration of mass on convex bodies (2006, background): “√ n for every convex body K. Klartag’s work [ Kl2 ]”
Logarithmic bounds for isoperimetry and slices of convex sets (2023, background): “For decades the best known bounds have been Ln ≤ Cn logn proven in Bourgain [7, 8] and Ln ≤ Cn proven in [28].”
Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach (2011, methodology): “(Zp(μ)) involving the “tilts” of the measure μ from [15, 16], and we relate between the Zp-bodies of the original measure and its tilts.”
Bourgain’s slicing problem and KLS isoperimetry up to polylog (2022, background): “For decades, the best estimate for Ln has been the bound Ln ≤ Cn1/4 where C > 0 is a universal constant, as proven in Bourgain [9, 10] (up to a logarithmic factor) and in [29].”
Uniform almost sub-Gaussian estimates for linear functionals on convex sets (2007, methodology): “Our main technical tool here is the logarithmic Laplace transform, as in our previous work [ 20 ].”
Entropy jumps for isotropic log-concave random vectors and spectral gap (2012, background): “See [2, 19, 18, 12] for background, equivalent formulations and related results.”
Small ball probability estimates, ψ2-behavior and the hyperplane conjecture (2010, methodology): “The second one is weaker than Klartag’s 4 √ n-bound in [8]; nevertheless, our method has the advantage that it can take into account any additional information on the ψα behavior of K.”
Invariances in variance estimates (2011, background): “The best known upper bound is due to Klartag [24]: L(d) ≤ cd.”