Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Petros Valettas"'
Autor:
Petros Valettas, Grigoris Paouris
Publikováno v:
Advances in Geometry. 19:165-189
We introduce and initiate the study of new parameters associated with any norm and any log-concave measure on $\mathbb R^n$, which provide sharp distributional inequalities. In the Gaussian context this investigation sheds light to the importance of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f25a0e248ae0bc6169e52f45f6decb5c
https://doi.org/10.1515/advgeom-2018-0030
https://doi.org/10.1515/advgeom-2018-0030
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
Autor:
Grigoris Paouris, Petros Valettas
Publikováno v:
Journal of Functional Analysis. 275:2225-2252
We prove that for any 2 p ∞ and for every n-dimensional subspace X of L p , represented on R n , whose unit ball B X is in Lewis' position one has the following two-level Gaussian concentration inequality: P ( | ‖ Z ‖ − E ‖ Z ‖ | > e E
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7964f1212d9a2c44eb4795bc54a6ca08
https://doi.org/10.1016/j.jfa.2018.07.008
https://doi.org/10.1016/j.jfa.2018.07.008
Publikováno v:
Stochastic Processes and their Applications. 127:3187-3227
We study the dependence on e in the critical dimension k ( n , p , e ) for which one can find random sections of the l p n -ball which are ( 1 + e ) -spherical. We give lower (and upper) estimates for k ( n , p , e ) for all eligible values p and e a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1413ecd06b16323a508d54a7347827cb
https://doi.org/10.1016/j.spa.2017.02.007
https://doi.org/10.1016/j.spa.2017.02.007
Autor:
Grigoris Paouris, Petros Valettas
We use probabilistic, topological and combinatorial methods to establish the following deviation inequality: For any normed space $X=(\mathbb R^n ,\|\cdot\| )$ there exists an invertible linear map $T:\mathbb R^n \to \mathbb R^n$ with \[ \mathbb P\le
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b2164db21e304f003a68448bf6a983a
Autor:
Petros Valettas
The concentration of measure phenomenon in Gauss' space states that every $L$-Lipschitz map $f$ on $\mathbb R^n$ satisfies \[ \gamma_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \} \right) \leqslant 2 e^{ - \frac{t^2}{ 2L^2} }, \quad t>0, \] where $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4fb2f157f2c3de488d64b209c5da56a2
Autor:
Grigoris Paouris, Petros Valettas
Publikováno v:
Journal of Functional Analysis. 267:3427-3443
We show that for any isotropic log-concave probability measure μ on R n , for every e > 0 , every 1 ⩽ k ⩽ n and any E ∈ G n , k there exists F ∈ G n , k with d ( E , F ) e and L π F μ C / e .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cedba7a62f3bb8a4f12c9cdbb2e6f9b0
https://doi.org/10.1016/j.jfa.2014.07.004
https://doi.org/10.1016/j.jfa.2014.07.004
We provide general inequalities that compare the surface area S(K) of a convex body K in ${\mathbb R}^n$ to the minimal, average or maximal surface area of its hyperplane or lower dimensional projections. We discuss the same questions for all the que
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5eecd63c8ad06c62ff61ab533cbe728b
Autor:
Grigoris Paouris, Petros Valettas
Publikováno v:
Ann. Probab. 46, no. 3 (2018), 1441-1454
Let $Z$ be an $n$-dimensional Gaussian vector and let $f: \mathbb R^n \to \mathbb R$ be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm Var} f(Z)} \right) \leq \exp(-ct^2),$$ for all $t>1$, where $c>0$ is an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f91e47d133a1602f9d19e760bdb2bdb