Small ball probability estimates, ψ2-behavior and the hyperplane conjecture

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Minkowski valuations intertwining the special linear group (2012, unknown): “, [18, 19, 53]), information theory (see, e.”
THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, methodology): “ has also provided tools for attacks on major unsolved problems such as the slicing problem of Bourgain, and consolidated connections between convex geometry and information theory. See, for example, [4], [13], [14], [21], [22], [23], [24], [26], and [35]. The other extension of interest here is the”
Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach (2011, methodology): “see Bourgain [8] and Klartag [15]). In the case α= 2, Theorem 1.1 yields LK ≤ Cb2. This slightly improves upon the previously known bound, which is: LK ≤ Cb2 p logb2 , (1.2) due to Dafnis and Paouris [11] in the precise form (1.2) and to Bourgain [9] (with a diﬀerent power of the logarithmic factor)”