Higher order concentration of measure

Bobkov SC, Götze F, Sambale H (2019)
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 21(3): 1850043.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d - 1 for any d is an element of N. The bounds are based on dth order derivatives or difference operators. In particular, we consider deviations of functions of independent random variables and differentiable functions over probability measures satisfying a logarithmic Sobolev inequality, and functions on the unit sphere. Applications include concentration inequalities for U-statistics as well as for classes of symmetric functions via polynomial approximations on the sphere (Edgeworth-type expansions).
Stichworte
Concentration of measure phenomenon; logarithmic Sobolev inequalities; Hoeffding decomposition; functions on the discrete cube; Efron-Stein; inequality
Erscheinungsjahr
2019
Zeitschriftentitel
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
Band
21
Ausgabe
3
Art.-Nr.
1850043
ISSN
0219-1997
eISSN
1793-6683
Page URI
https://pub.uni-bielefeld.de/record/2935874

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Bobkov SC, Götze F, Sambale H. Higher order concentration of measure. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. 2019;21(3): 1850043.
Bobkov, S. C., Götze, F., & Sambale, H. (2019). Higher order concentration of measure. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 21(3), 1850043. doi:10.1142/S0219199718500438
Bobkov, S. C., Götze, F., and Sambale, H. (2019). Higher order concentration of measure. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 21:1850043.
Bobkov, S.C., Götze, F., & Sambale, H., 2019. Higher order concentration of measure. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 21(3): 1850043.
S.C. Bobkov, F. Götze, and H. Sambale, “Higher order concentration of measure”, COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 21, 2019, : 1850043.
Bobkov, S.C., Götze, F., Sambale, H.: Higher order concentration of measure. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. 21, : 1850043 (2019).
Bobkov, Sergey C., Götze, Friedrich, and Sambale, Holger. “Higher order concentration of measure”. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 21.3 (2019): 1850043.