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The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin’s local time identity
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  • Published: 25 March 2004

The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin’s local time identity

  • David Aldous1,
  • Grégory Miermont2 &
  • Jim Pitman1 

Probability Theory and Related Fields volume 129, pages 182–218 (2004)Cite this article

  • 218 Accesses

  • 19 Citations

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Abstract.

We study the inhomogeneous continuum random trees (ICRT) that arise as weak limits of birthday trees. We give a description of the exploration process, a function defined on [0,1] that encodes the structure of an ICRT, and also of its width process, determining the size of layers in order of height. These processes turn out to be transformations of bridges with exchangeable increments, which have already appeared in other ICRT related topics such as stochastic additive coalescence. The results rely on two different constructions of birthday trees from processes with exchangeable increments, on weak convergence arguments, and on general theory on continuum random trees.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of California, 367 Evans Hall, #3860, Berkeley, CA 94720-3860, USA

    David Aldous & Jim Pitman

  2. DMA, École Normale Supérieure and LPMA, Université Paris, 6. 45 rue d’Ulm, 75230, Paris Cedex OS, France

    Grégory Miermont

Authors
  1. David Aldous
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  2. Grégory Miermont
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  3. Jim Pitman
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Additional information

D. Aldous: Research supported in part by N.S.F. Grant DMS-0203062

J. Pitman: Research supported in part by N.S.F. Grant DMS-0071448

Mathematics Subject Classification (2000): 60C05, 60F17, 60G09, 60G51

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Aldous, D., Miermont, G. & Pitman, J. The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin’s local time identity. Probab. Theory Relat. Fields 129, 182–218 (2004). https://doi.org/10.1007/s00440-003-0334-7

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  • Received: 09 May 2003

  • Revised: 02 November 2003

  • Published: 25 March 2004

  • Issue Date: June 2004

  • DOI: https://doi.org/10.1007/s00440-003-0334-7

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Keywords

  • Continuum random tree
  • Exchangeable increments
  • Exploration process
  • Lévy process
  • Weak convergence
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