A Bernstein—Chernoff deviation inequality, and geometric properties of random families of operators |
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Authors: | Shiri Artstein-Avidan |
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Institution: | (1) Department of Mathematics, Princeton University, Fine Hall, Washington Road, 08544-1000 Princeton, NJ, USA |
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Abstract: | In this paper we first describe a new deviation inequality for sums of independent random variables which uses the precise
constants appearing in the tails of their distributions, and can reflect in full their concentration properties. In the proof
we make use of Chernoff's bounds. We then apply this inequality to prove a global diameter reduction theorem for abstract
families of linear operators endowed with a probability measure satisfying some condition. Next we give a local diameter reduction
theorem for abstract families of linear operators. We discuss some examples and give one more global result in the reverse
direction, and extensions.
This research was partially supported by BSF grant 2002-006. |
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Keywords: | |
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