Search: All articles in the CMB digital archive with keyword random'' Euclidean section
 Euclidean Sections of Direct Sums of Normed Spaces We study the dimension of random'' Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from \cite{LMS}, to show that for the direct sums the standard randomness with respect to the Haar measure on Grassmanian coincides with a much weaker'' randomness of diagonal'' subspaces (Corollary~\ref{sle} and explanation after). We also add some relative information on phase transition''. Keywords:Dvoretzky theorem, random'' Euclidean section, phase transition in asymptotic convexityCategories:46B07, 46B09, 46B20, 52A21