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Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees
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  • Published: 14 July 2005

Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees

  • David Aldous1,
  • Grégory Miermont2 &
  • Jim Pitman3 

Probability Theory and Related Fields volume 133, pages 1–17 (2005)Cite this article

  • 112 Accesses

  • 9 Citations

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Abstract

We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of “attracting points” to emerge.

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References

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Author information

Authors and Affiliations

  1. Department of Statistics, U.C. Berkeley, CA, 94720-3860, USA

    David Aldous

  2. CNRS, Université Paris-Sud, Bât. 425, 91405, Orsay, France

    Grégory Miermont

  3. Department of Statistics, U.C. Berkeley, CA, 94720-3860, USA

    Jim Pitman

Authors
  1. David Aldous
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  2. Grégory Miermont
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  3. Jim Pitman
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Corresponding author

Correspondence to David Aldous.

Additional information

Research supported by NSF Grant DMS-0203062.

Research supported by NSF Grant DMS-0071468.

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Cite this article

Aldous, D., Miermont, G. & Pitman, J. Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees. Probab. Theory Relat. Fields 133, 1–17 (2005). https://doi.org/10.1007/s00440-004-0407-2

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  • Received: 19 February 2004

  • Revised: 26 October 2004

  • Published: 14 July 2005

  • Issue Date: September 2005

  • DOI: https://doi.org/10.1007/s00440-004-0407-2

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Mathematics Subject Classification (2000)

  • 60C05
  • 60F17

Key words or phrases

  • Random mapping
  • Weak convergence
  • Inhomogeneous continuum random tree
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