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

Abstract

AbstractUsing 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 at the point x. As one application, we obtain a deviation inequality for the number of k‐cycles in a random graph. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004