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

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DOI

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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     author = {Litvak, A. E. and Milman, V. D.},
     title = {Euclidean {Sections} of {Direct} {Sums} of {Normed} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {242--251},
     year = {2003},
     volume = {46},
     number = {2},
     doi = {10.4153/CMB-2003-024-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-024-8/}
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