Geodesic
Phenomena arising from high dimensionality
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 1, pp. 159-169

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Some general properties are discussed for normed spaces (or, equivalently, convex bodies) that are finite-dimensional of very high dimension. It turns out that these objects show much less diversity than one could expect a priori. Next, some asymptotic phenomena that govern (in the author's opinion) the asymptotic behaviour of systems of large dimension are analyzed. 
@article{RM_2004_59_1_a10,
     author = {V. D. Milman},
     title = {Phenomena arising from high dimensionality},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {159--169},
     publisher = {mathdoc},
     volume = {59},
     number = {1},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2004_59_1_a10/}
}
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V. D. Milman. Phenomena arising from high dimensionality. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 1, pp. 159-169. http://geodesic.mathdoc.fr/item/RM_2004_59_1_a10/