Higher order concentration of measure

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

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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).
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Zeitschriftentitel
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
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21
Ausgabe
3
Art.-Nr.
1850043
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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.