Powiadomienia systemowe
- Sesja wygasła!
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We study concentration properties for vector-valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in R^k. To this end, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions with earlier results by Pinelis in the Gaussian case, and discuss extensions to the infinite-dimensional setting.
Wydawca
Rocznik
Tom
Strony
261--278
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
autor
- Institut de Mathematiques, Universite Paul-Sabatier, 31062 Toulouse, France, ledoux@math.ups-tlse.fr
Bibliografia
- [1] F. Barthe, Extremal properties of central half-spaces for product measures, J. Funct. Anal. 182 (2001), 81-107.
- [2] Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure Appl. Math. 44 (1991), 375-417.
- [3] L. Caffarelli, Monotonicity properties of optimal transportation and the FKG and related inequalities, Comm. Math. Phys. 214 (2000), 547-563.
- [4] M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhauser, 1998.
- [5] M. Gromov, Isoperimetry of waists and concentration of maps, Geom. Funct. Anal. 13 (2003), 178-215.
- [6] S. Kwapień and W. A. Woyczyński, Random Series and Stochastic Integrals: Single and Multiple, Probab. Appl., Birkhauser, 1992.
- [7] R. Latała and K. Oleszkiewicz, Small ball probability estimates in terms of width, Studia Math. 169 (2005), 305-314.
- [8] M. Ledoux, The Concentration of Measure Phenomenon, Math. Surveys Monogr. 89, Amer. Math. Soc., 2001.
- [9] M. Ledoux and M. Talagrand, Probability in Banach Spaces. Isoperimetry and Processes, Ergeb. Math. Grenzgeb. (3) 23, Springer, 1991.
- [10] I. Pinelis, Optimal tail comparison based on comparison of moments, in: High Dimensional Probability (Oberwolfach, 1996), Progr. Probab. 43, Birkhauser, 1998, 297-314.
- [11] G. Pisier, Probabilistic methods in the geometry of Banach spaces, in: Probability and Analysis (Varenna, 1985), Lecture Notes in Math. 1206, Springer, 1986, 167-241.
- [12] G. R. Shorack and J. A. Wellner, Empirical Processes with Applications to Statistics, Wiley, New York, 1986.
- [13] M. Talagrand, Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem, Geom. Funct. Anal. 3 (1993), 295-314.
- [14] —, The Generic Chaining. Upper and Lower Bounds of Stochastic Processes, Springer Monogr. Math., Springer, Berlin, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0017-0094