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Strata of random mappings - A combinatorial approach

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  • Drmota, Michael
  • Gittenberger, Bernhard

Abstract

Consider the functional graph of a random mapping from an n-element set into itself. Then the number of nodes in the strata of this graph can be viewed as stochastic process. Using a generating function approach it is shown that a suitable normalization of this process converges weakly to local time of reflecting Brownian bridge.

Suggested Citation

  • Drmota, Michael & Gittenberger, Bernhard, 1999. "Strata of random mappings - A combinatorial approach," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 157-171, August.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:2:p:157-171
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    References listed on IDEAS

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    1. J. W. Cohen & G. Hooghiemstra, 1981. "Brownian Excursion, the M / M /1 Queue and Their Occupation Times," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 608-629, November.
    2. Gutjahr, W. & Pflug, G. Ch., 1992. "The asymptotic contour process of a binary tree is a Brownian excursion," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 69-89, May.
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    Cited by:

    1. David Clancy, 2021. "The Gorin–Shkolnikov Identity and Its Random Tree Generalization," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2386-2420, December.

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