Convergence of bi-measure R-tree and the pruning process
type: Dataset
description: In [Aldous,Pitman,1998] a tree-valued Markov chain is derived by pruning off more and more subtrees along the edges of a Galton-Watson tree. More recently, in [Abraham,Delmas,2012], a continuous analogue of the tree-valued pruning dynamics is constructed along Lévy trees. In the present paper, we provide a new topology which allows to link the discrete and the continuous dynamics by considering them as instances of the same strong Markov process with different initial conditions. We construct this pruning process on the space of so-called bi-measure trees, which are metric measure spaces with an additional pruning measure. The pruning measure is assumed to be finite on finite trees, but not necessarily locally finite. We also characterize the pruning process analytically via its Markovian generator and show that it is continuous in the initial bi-measure tree. A series of examples is given, which include the finite variance offspring case where the pruning measure is the length measure on the underlying tree.
issued: 2026-05-07T07:47:34.609608
language: en
modified: 2026-05-07T07:47:34.609613
contact point: Organization
  fn: CCSD
keyword: 60f05-60b12-60j25-05c05-05c10-60g55
keyword: crt
keyword: infoeu-reposemanticspreprint
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: non-locally-finite-measures
keyword: pointed-gromov-weak-topology
keyword: preprints-working-papers-
keyword: prohorov-metric
keyword: pruning-procedure
keyword: real-trees
keyword: tree-valued-markov-process
landing page: https://hal.science/hal-00815760

Convergence of bi-measure R-tree and the pruning process
type: Distribution
format: HTML
issued: 2026-05-07T07:47:34.610936
modified: 2026-05-07T07:47:34.597282
access URL: https://hal.science/hal-00815760

test_moissonnage_selune
type: Agent