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Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing

  • Larry Goldstein (a1)

Abstract

Berry-Esseen-type bounds to the normal, based on zero- and size-bias couplings, are derived using Stein's method. The zero biasing bounds are illustrated in an application to combinatorial central limit theorems in which the random permutation has either the uniform distribution or one that is constant over permutations with the same cycle type, with no fixed points. The size biasing bounds are applied to the occurrences of fixed, relatively ordered subsequences (such as rising sequences) in a random permutation, and to the occurrences of patterns, extreme values, and subgraphs in finite graphs.

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Corresponding author

Postal address: Department of Mathematics, University of Southern California, 3620 Vermont Avenue, KAP 108, Los Angeles, CA 90089-2532, USA. Email address: larry@math.usc.edu

References

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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