On concentration of distributions of random weighted sums

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A central limit theorem for convex sets (2006, methodology): “Our next proposition is essentially taken from Anttila, Ball and Perissinaki [1], yet we use the extension to the non-even case which is a particular case of a result of Bobkov [4, Proposition 3.1].”
An optimal lower bound on the communication complexity of gap-hamming-distance (2010, unknown): “The ﬁrst is in work by Sudakov [Sud78] and Diaconis and Freedman [DF84] (see also [Bob03] for a more recent exposition) who showed that for any random variable in R n with zero mean and identity covariance matrix whose norm is concentrated around √ n , almost all its projections are close to the…”
Convex bodies and norms associated to convex measures (2010, background): “Grunbaum’s theorem. In the log-concave case, Theorem 5.2 also appeared in [ 10 ], Lemma 3.3.”
A Berry-Esseen type inequality for convex bodies with an unconditional basis (2007, background): “The existence of suchu ∈ D is a consequence of the classical existence and regularity theory of the Neumann problem for the Laplacian on domains with aC∞smooth boundary (see, e.g., Folland’s book [16, chapter 7]).”
Uniform almost sub-Gaussian estimates for linear functionals on convex sets (2007, background): “Recall that µ({x 2 Rn;|’(x)| k ’kL1(µ)}) 1 c (see, e.g., the methods in [ 3, section 3 ]).”