Deviation inequality for monotonic Boolean functions with application to a number of k-cycles in a random graph

Details Deviation inequality for monotonic Boolean functions with application to a number of k-cycles in a random graph Deviation inequality for monotonic Boolean functions with application to a number of k-cycles in a random graph

2004-05-18

arxiv.org/abs/math/0405355v1

2004 Rand. Structures Algorithms 24 No. 1

Mathematics

Probability

11 pages, 1 figure

Scientific paper

Using Talagrand's concentration inequality on the discrete cube {0,1}^m we show that given a real-valued function Z(x)on {0,1}^m that satisfies certain monotonicity conditions one can control the deviations of Z(x) above its median by a local Lipschitz norm of Z(x) at the point x. As one application, we give a simple proof of a nearly optimal deviation inequality for the number of k-cycles in a random graph.

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