Volumetric invariants and operators on random families
of Banach spaces
Studia Mathematica, Tome 159 (2003) no. 2, pp. 315-335
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The geometry of random projections of centrally symmetric convex bodies in
${ \mathbb R}^N$ is studied. It is shown that if for such a body $K$ the Euclidean ball $B_2^N$ is the ellipsoid of minimal volume containing it and a random $n$-dimensional projection $B=P_H(K)$ is “far” from $P_H(B_2^N)$ then the (random) body $B$ is as “rigid” as its “distance” to $P_H(B_2^N)$ permits. The result holds for the full range of dimensions $1 \le n \le \lambda N$, for arbitrary $\lambda \in (0,1)$.
Keywords:
geometry random projections centrally symmetric convex bodies mathbb studied shown body euclidean ball ellipsoid minimal volume containing random n dimensional projection k far random body rigid its distance permits result holds full range dimensions lambda arbitrary lambda
Affiliations des auteurs :
Piotr Mankiewicz 1 ; Nicole Tomczak-Jaegermann 2
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author = {Piotr Mankiewicz and Nicole Tomczak-Jaegermann},
title = {Volumetric invariants and operators on random families
of {Banach} spaces},
journal = {Studia Mathematica},
pages = {315--335},
publisher = {mathdoc},
volume = {159},
number = {2},
year = {2003},
doi = {10.4064/sm159-2-10},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm159-2-10/}
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Piotr Mankiewicz; Nicole Tomczak-Jaegermann. Volumetric invariants and operators on random families of Banach spaces. Studia Mathematica, Tome 159 (2003) no. 2, pp. 315-335. doi: 10.4064/sm159-2-10
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