Almost Euclidean sections in symmetric spaces and concentration of order statistics

作者：Tikhomirov Konstantin E^*

来源：Journal of Functional Analysis, 2013, 265(9): 2074-2088.

DOI：10.1016/j.jfa.2013.06.008

• Dvoretzky's theorem
• Symmetric basis
• Order statistic

We prove that for any symmetric n-dimensional normed space E and any epsilon > 0, E contains a (1 + epsilon)-Euclidean subspace of dimension at least c Inn/In(1/epsilon), where c is an absolute constant. The proof is based on a concentration property of order statistics of random vectors with i.i.d. coordinates.

• 出版日期2013-11-1