Geodesic
Volumetric invariants and operators on random families of Banach spaces
Piotr Mankiewicz1 ; Nicole Tomczak-Jaegermann2
1Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-956 Warszawa, Poland
2Department of Mathematical and Statistical Sciences University of Alberta Edmonton, Alberta Canada T6G 2G1
Studia Mathematica, Tome 159 (2003) no. 2, pp. 315-335
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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 $\lambda \in (0,1)$.
DOI : 10.4064/sm159-2-10
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

Piotr Mankiewicz  1   ; Nicole Tomczak-Jaegermann  2

1 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-956 Warszawa, Poland
2 Department of Mathematical and Statistical Sciences University of Alberta Edmonton, Alberta Canada T6G 2G1 
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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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