Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Carsten Schütt"'
Publikováno v:
Discrete & Computational Geometry. 69:453-504
The convex hull of N independent random points chosen on the boundary of a simple polytope in $$ {\mathbb {R}}^n$$ R n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume differen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cb8d153d92e5f59a59b331a752786412
https://doi.org/10.1007/s00454-022-00460-2
https://doi.org/10.1007/s00454-022-00460-2
Affine invariant points and maps for sets were introduced by Gr\"unbaum to study the symmetry structure of convex sets. We extend these notions to a functional setting. The role of symmetry of the set is now taken by evenness of the function. We show
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e83428d196512577539b184792ee6c8a
Publikováno v:
Advances in Mathematics. 338:912-952
We investigate weighted floating bodies of polytopes. We show that the weighted volume depends on the complete flags of the polytope. This connection is obtained by introducing flag simplices, which translate between the metric and combinatorial stru
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::12880931ec1008a2e65fc1a936133d98
https://doi.org/10.1016/j.aim.2018.09.006
https://doi.org/10.1016/j.aim.2018.09.006
Publikováno v:
Journal of Functional Analysis. 273:471-495
In this work, we study the volume ratio of the projective tensor products $\ell^n_p\otimes_{\pi}\ell_q^n\otimes_{\pi}\ell_r^n$ with $1\leq p\leq q \leq r \leq \infty$. We obtain asymptotic formulas that are sharp in almost all cases. As a consequence
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::66865ee88c8c1b860bcabcc424085102
https://doi.org/10.1016/j.jfa.2017.03.019
https://doi.org/10.1016/j.jfa.2017.03.019
Publikováno v:
Statist. Surv. 13 (2019), 52-118
Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Maximum halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the ma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b588e0429de1d3325e347e874a5d0ac
https://projecteuclid.org/euclid.ssu/1561169006
https://projecteuclid.org/euclid.ssu/1561169006
Publikováno v:
Journal of Functional Analysis. 279:108531
Given a convex body K ⊆ R n and p ∈ R , we introduce and study the extremal inner and outer affine surface areas I S p ( K ) = sup K ′ ⊆ K ( as p ( K ′ ) ) and o s p ( K ) = inf K ′ ⊇ K ( as p ( K ′ ) ) , where as p ( K ′ )
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b9f6de6d0f80114b4336902e4f419782
https://doi.org/10.1016/j.jfa.2020.108531
https://doi.org/10.1016/j.jfa.2020.108531
Publikováno v:
Indiana University Mathematics Journal. 64:735-768
An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)). We define here the new notion of d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a6e374989f9511b9730021da23c8401
https://doi.org/10.1512/iumj.2015.64.5514
https://doi.org/10.1512/iumj.2015.64.5514
We introduce floating bodies for convex, not necessarily bounded subsets of $\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of the integra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a9e9f1afe0f0a838d991af57fd33c920
http://arxiv.org/abs/1711.11088
http://arxiv.org/abs/1711.11088
Autor:
Matthieu Fradelizi, Umut Caglar, Elisabeth M. Werner, Carsten Schütt, Olivier Guédon, Joseph Lehec
Publikováno v:
International Mathematics Research Notices
International Mathematics Research Notices, Oxford University Press (OUP), 2016, pp.1223-1250. ⟨10.1093/imrn/rnv151⟩
International Mathematics Research Notices, Oxford University Press (OUP), 2016, pp.1223-1250. ⟨10.1093/imrn/rnv151⟩
International audience; In contemporary convex geometry, the rapidly developing Lp-Brunn-Minkowski theory is a modern analogue of the classical Brunn-Minkowski theory. A central notion of this theory is the Lp-affine surface area of convex bodies. He
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::14acf510a9bab877ebf83c5d747d6d60
https://hal-upec-upem.archives-ouvertes.fr/hal-01262626
https://hal-upec-upem.archives-ouvertes.fr/hal-01262626
Publikováno v:
Canadian Mathematical Bulletin
Canadian Mathematical Bulletin, 2011, 55 (3), pp.498-508. ⟨10.4153/CMB-2011-142-1⟩
Canadian Mathematical Bulletin, Cambridge University Press, 2011, 55 (3), pp.498-508. ⟨10.4153/CMB-2011-142-1⟩
Canadian Mathematical Bulletin, 2011, 55 (3), pp.498-508. ⟨10.4153/CMB-2011-142-1⟩
Canadian Mathematical Bulletin, Cambridge University Press, 2011, 55 (3), pp.498-508. ⟨10.4153/CMB-2011-142-1⟩
We establish some inequalities for the second momentof a convex body K under various assumptions on the position of K.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::216bf2d45851c4569a3ac0bb7ea6b7c3
https://doi.org/10.4153/cmb-2011-142-1
https://doi.org/10.4153/cmb-2011-142-1