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Concentration

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Probabilistic Methods for Algorithmic Discrete Mathematics

Part of the book series: Algorithms and Combinatorics ((AC,volume 16))

Summary

Upper bounds on probabilities of large deviations for sums of bounded independent random variables may be extended to handle functions which depend in a limited way on a number of independent random variables. This ‘method of bounded differences’ has over the last dozen or so years had a great impact in probabilistic methods in discrete mathematics and in the mathematics of operational research and theoretical computer science. Recently Talagrand introduced an exciting new method for bounding probabilities of large deviations, which often proves superior to the bounded differences approach. In this chapter we introduce and survey these two approaches and some of their applications.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Oxford, UK

    Colin McDiarmid

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  1. Colin McDiarmid
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Editors and Affiliations

  1. LIRMM, 161, rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

  2. Department of Statistics, University of Oxford, 1 South Parks Road, OX1 3TG, Oxford, UK

    Colin McDiarmid

  3. Equipe Combinatoire, Université Pierre et Marie Curie, Paris 6 Case 189, 4, place Jussieu, 75252, Paris Cedex 5, France

    Jorge Ramirez-Alfonsin  & Bruce Reed  & 

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McDiarmid, C. (1998). Concentration. In: Habib, M., McDiarmid, C., Ramirez-Alfonsin, J., Reed, B. (eds) Probabilistic Methods for Algorithmic Discrete Mathematics. Algorithms and Combinatorics, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12788-9_6

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  • DOI: https://doi.org/10.1007/978-3-662-12788-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08426-3

  • Online ISBN: 978-3-662-12788-9

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