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We compute the number of summands in q-averages of norms needed to approximate an Euclidean norm. It turns out that these numbers depend on the norm involved essentially only through the maximal ratio of the norm and the Euclidean norm. Particular attention is given to the case q = 1 (in which the average is replaced with the maxima). This is closely(More)
Concentration inequalities are estimates for the degree of approximation of functions on metric probability spaces around their mean. It turns out that in many natural situations one can give very good such estimates, and that these are extremely useful. We survey here some of the main methods for proving such inequalities and give a few examples to the way(More)
×ØÖÖغ The best constant and the extreme cases in an inequality of H.P. Rosen-thal, relating the p moment of a sum of independent symmetric random variables to that of the p and 2 moments of the individual variables, are computed in the range 2 < p ≤ 4. This complements the work of Utev who has done the same for p > 4. The qualitative nature of the extreme(More)
MAX CUT is the problem of partitioning the vertices of a graph into two sets, maximizing the number of edges joining these sets. This problem is NP-hard. Goemans and Williamson proposed an algorithm that first uses a semidefinite programming relaxation of MAX CUT to embed the vertices of the graph on the surface of an <italic>n</italic> dimensional sphere,(More)