13 research outputs found
Combinatorial Inequalities and Subspaces of L1
Let M and N be Orlicz functions. We establish some combinatorial inequalities
and show that the product spaces l^n_M(l^n_N) are uniformly isomorphic to
subspaces of L_1 if M and N are "separated" by a function t^r, 1<r<2
Data depth and floating body
Little known relations of the renown concept of the halfspace depth for
multivariate data with notions from convex and affine geometry are discussed.
Halfspace depth may be regarded as a measure of symmetry for random vectors. As
such, the depth stands as a generalization of a measure of symmetry for convex
sets, well studied in geometry. Under a mild assumption, the upper level sets
of the halfspace depth coincide with the convex floating bodies used in the
definition of the affine surface area for convex bodies in Euclidean spaces.
These connections enable us to partially resolve some persistent open problems
regarding theoretical properties of the depth
Affine invariant points and their duals
Non UBCUnreviewedAuthor affiliation: Christian-Albrechts-UniversitaetFacult
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Non UBCUnreviewedAuthor affiliation: Christian-Albrechts-UniversitaetFacult
On the geometry of projective tensor products
we study the volume ratio of the projective tensor products with . The asymptotic formulas we obtain are sharp in almost all cases. As a consequence of our estimates, these spaces allow for an almost Euclidean decomposition of Kashin type whenever or and . Also, from the Bourgain-Milman bound on the volume ratio of Banach spaces in terms of their cotype constant, we obtain information on the cotype of these -fold projective tensor products. Our results naturally generalize to the -fold products with and . Joint work with
Giladi, Prochno, Tomczak-Jaegermann and Werner.Non UBCUnreviewedAuthor affiliation: Christian-Albrechts-UniversitaetFacult