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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2013

Record process on the Continuum Random Tree

Résumé

By considering a continuous pruning procedure on Aldous's Brownian tree, we construct a random variable $\Theta$ which is distributed, conditionally given the tree, according to the probability law introduced by Janson as the limit distribution of the number of cuts needed to isolate the root in a critical Galton-Watson tree. We also prove that this random variable can be obtained as the a.s. limit of the number of cuts needed to cut down the subtree of the continuum tree spanned by $n$ leaves.
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Dates et versions

hal-00609467 , version 1 (19-07-2011)
hal-00609467 , version 2 (04-06-2012)
hal-00609467 , version 3 (01-02-2013)

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Romain Abraham, Jean-François Delmas. Record process on the Continuum Random Tree. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2013, 10, pp.251. ⟨hal-00609467v3⟩
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