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RSA

2002

2002

Let be a finite index set and k 1 a given integer. Let further S []k be an arbitrary family of k element subsets of . Consider a (binomial) random subset p of , where p = (pi : i ) and a random variable X counting the elements of S that are contained in this random subset. In this paper we survey techniques of obtaining upper bounds on the upper tail probabilities P(X + t) for t > 0. Seven techniques, ranging from Azuma's inequality to the purely combinatorial deletion method, are described, illustrated and compared against each other for a couple of typical applications. As one application, we obtain essentially optimal bounds for the upper tails for the numbers of subgraphs isomorphic to K4 or C4 in a random graph G(n, p), for certain ranges of p.

Related Content

Added |
23 Dec 2010 |

Updated |
23 Dec 2010 |

Type |
Journal |

Year |
2002 |

Where |
RSA |

Authors |
Svante Janson, Andrzej Rucinski |

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