Geodesic
Euclidean Sections of Direct Sums of Normed Spaces
Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 242-251

Voir la notice de l'article provenant de la source Cambridge University Press

We study the dimension of “random” Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from $[\text{LMS}]$ , 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 1.4 and explanation after). We also add some relative information on “phase transition”.
DOI : 10.4153/CMB-2003-024-8
Mots-clés : 46B07, 46B09, 46B20, 52A21, Dvoretzky theorem, “random” Euclidean section, phase transition in asymptotic convexity 
Litvak, A. E.; Milman, V. D. Euclidean Sections of Direct Sums of Normed Spaces. Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 242-251. doi: 10.4153/CMB-2003-024-8
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