We compare various constructions of random proportional quotients of (i.e., with the dimension of the quotient roughly equal to a fixed proportion of m as m → ∞) and show that several of those constructions are equivalent. As a consequence of our approach we conclude that the most natural “geometric” models possess a number of asymptotically extremal properties, some of which were hitherto not known for any model.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-1-4,
author = {Piotr Mankiewicz and Stanis\l aw J. Szarek},
title = {On the geometry of proportional quotients of $l1^{m}$
},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {51-66},
zbl = {1017.46005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-1-4}
}
Piotr Mankiewicz; Stanisław J. Szarek. On the geometry of proportional quotients of $l₁^{m}$
. Studia Mathematica, Tome 157 (2003) pp. 51-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-1-4/