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Dvoretzky Type Theorems for Subgaussian Coordinate Projections

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  • Shahar Mendelson

    (Technion, I.I.T)

Abstract

Given a class of functions F on a probability space $$(\Omega ,\mu )$$ ( Ω , μ ) , we study the structure of a typical coordinate projection of the class, defined by $$\{(f(X_i))_{i=1}^N : f \in F\}$$ { ( f ( X i ) ) i = 1 N : f ∈ F } , where $$X_1,\ldots ,X_N$$ X 1 , … , X N are independent, selected according to $$\mu $$ μ . We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.

Suggested Citation

  • Shahar Mendelson, 2016. "Dvoretzky Type Theorems for Subgaussian Coordinate Projections," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1644-1660, December.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:4:d:10.1007_s10959-015-0624-x
    DOI: 10.1007/s10959-015-0624-x
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