Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Empirical processes with bounded \psi_1 diameter   We study the empirical process indexed by F^2=\{f^2 : f \in F\}, where F is a
class of mean-zero functions on a probability space. We present a sharp bound
on the supremum of that process which depends on the \psi_1 diameter of the
class F (rather than on the \psi_2 one) and on the complexity parameter
\gamma_2(F,\psi_2). In addition, we present optimal bounds on the random
diameters \sup_{f \in F} \max_{|I|=m} (\sum_{i \in I} f^2(X_i))^{1/2} using the
same parameters. As applications, we extend several well known results in
Asymptotic Geometric Analysis to any isotropic, log-concave ensemble on R^n.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th