We study the deviation probability P{|∥X∥-E∥X∥|>t} where X is a ϕ-subgaussian random element taking values in the Hilbert space l2 and ϕ(x) is an N-function. It is shown that the order of this deviation is exp{-ϕ*(Ct)}, where C depends on the sum of ϕ-subgaussian standard of the coordinates of the random element X and ϕ*(x) is the Young–Fenchel transform of ϕ(x). An application to the classically subgaussian random variables (ϕ(x)=x2/2) is given.

### On the Concentration Phenomenon for phi-subgaussian Random Elements

#### Abstract

We study the deviation probability P{|∥X∥-E∥X∥|>t} where X is a ϕ-subgaussian random element taking values in the Hilbert space l2 and ϕ(x) is an N-function. It is shown that the order of this deviation is exp{-ϕ*(Ct)}, where C depends on the sum of ϕ-subgaussian standard of the coordinates of the random element X and ϕ*(x) is the Young–Fenchel transform of ϕ(x). An application to the classically subgaussian random variables (ϕ(x)=x2/2) is given.
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2006
Giuliano, Rita; TIEN CHUNG, Hu; A., Volodin
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/106533
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