Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Peter Pivovarov"'
Autor:
Thomas Hack, Peter Pivovarov
Publikováno v:
Mathematika. 67:100-115
As a natural analog of Urysohn's inequality in Euclidean space, Gao, Hug, and Schneider showed in 2003 that in spherical or hyperbolic space, the total measure of totally geodesic hypersurfaces meeting a given convex body K is minimized when K is a g
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9893b9782e30109e84d9ab28aaae1731
https://doi.org/10.1112/mtk.12063
https://doi.org/10.1112/mtk.12063
Publikováno v:
IEEE Transactions on Information Theory. 66:2898-2903
In this note we study a conjecture of Madiman and Wang which predicted that the generalized Gaussian distribution minimizes the Renyi entropy of the sum of independent random variables. Through a variational analysis, we show that the generalized Gau
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::076f0a065f090e3d035de79502e8906d
https://doi.org/10.1109/tit.2019.2961080
https://doi.org/10.1109/tit.2019.2961080
Publikováno v:
Journal of Mathematical Sciences. 238:537-559
We study linear images of a symmetric convex body C ⊆ ℝN under an n × N Gaussian random matrix G, where N ≥ n. Special cases include common models of Gaussian random polytopes and zonotopes. We focus on the intrinsic volumes of GC and study th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d7cdabdf2b6e4029a5e1073cf32f3a1a
https://doi.org/10.1007/s10958-019-04256-3
https://doi.org/10.1007/s10958-019-04256-3
Publikováno v:
Transactions of the American Mathematical Society. 371:3309-3324
Alexandrov’s inequalities imply that for any convex body A A , the sequence of intrinsic volumes V 1 ( A ) , … , V n ( A ) V_1(A),\ldots ,V_n(A) is non-increasing (when suitably normalized). Milman’s random version of Dvoretzky’s theorem show
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7bc97bf1d9322b97cdbf2d6102f1c445
https://doi.org/10.1090/tran/7413
https://doi.org/10.1090/tran/7413
Publikováno v:
Israel Journal of Mathematics. 216:877-889
We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if f is a probability density on R n of the form f(x) = П =1 f i (x i ), where each f i is a density on R, say bounded by one, then the den
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77253e7adcfd70a3404ce48a1050e4f9
https://doi.org/10.1007/s11856-016-1431-5
https://doi.org/10.1007/s11856-016-1431-5
Publikováno v:
Proceedings of the London Mathematical Society. 113:140-162
Let $\mu$ be a probability measure on $\mathbb{R}^n$ with a bounded density $f$. We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trad
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01f4231eb8280ac2125150fc936acacf
https://doi.org/10.1112/plms/pdw026
https://doi.org/10.1112/plms/pdw026
Autor:
Jesus Rebollo Bueno, Peter Pivovarov
Publikováno v:
Communications in Contemporary Mathematics. 23:2050019
The Brunn–Minkowski and Prékopa–Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions so it seems that convexity has no special sig
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::be8bc76c580c289f555880e15fc9c189
https://doi.org/10.1142/s0219199720500194
https://doi.org/10.1142/s0219199720500194
Autor:
Peter Pivovarov, Grigoris Paouris
Publikováno v:
Convexity and Concentration ISBN: 9781493970049
We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their various extensions. We show that many such inequalities admit stronger
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b531d91feb10a9ec679512cdc503af43
https://doi.org/10.1007/978-1-4939-7005-6_13
https://doi.org/10.1007/978-1-4939-7005-6_13
Autor:
Grigoris Paouris, Peter Pivovarov
Publikováno v:
Discrete & Computational Geometry. 49:601-646
We prove small-deviation estimates for the volume of random convex sets. The focus is on convex hulls and Minkowski sums of line segments generated by independent random points. The random models considered include (Lebesgue) absolutely continuous pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ba2d95e1f20d85c81ac48ecb49d8278f
https://doi.org/10.1007/s00454-013-9492-2
https://doi.org/10.1007/s00454-013-9492-2
Autor:
Grigoris Paouris, Peter Pivovarov
Publikováno v:
Proceedings of the American Mathematical Society. 141:1805-1808
It is shown that intrinsic volumes of a convex body decrease under linear contractions. Let C ⊂ R be a convex body and B 2 the Euclidean ball in R . The Steiner formula expresses the volume of the Minkowski sum C + eB 2 in terms of the intrinsic vo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::065852a07ed58b3cb673a707ec211438
https://doi.org/10.1090/s0002-9939-2012-11494-7
https://doi.org/10.1090/s0002-9939-2012-11494-7