Abstract
Given a class of functions F on a probability space \((\Omega ,\mu )\), we study the structure of a typical coordinate projection of the class, defined by \(\{(f(X_i))_{i=1}^N : f \in F\}\), where \(X_1,\ldots ,X_N\) are independent, selected according to \(\mu \). We show that when F is a subgaussian class, a typical coordinate projection satisfies a Dvoretzky type theorem.
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Notes
More details on gaussian processes and their properties may be found in the book [1], which contains a detailed survey on this topic.
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Supported in part by the Mathematical Sciences Institute, The Australian National University, Canberra, ACT 2601, Australia. Additional support was given by an Israel Science Foundation Grant.
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Mendelson, S. Dvoretzky Type Theorems for Subgaussian Coordinate Projections. J Theor Probab 29, 1644–1660 (2016). https://doi.org/10.1007/s10959-015-0624-x
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DOI: https://doi.org/10.1007/s10959-015-0624-x