The forest associated with the record process on a L\'evy tree
Romain Abraham (MAPMO), Jean-Francois Delmas (CERMICS)

TL;DR
This paper studies a pruning and regrafting process on Le9vy trees, showing the resulting tree's distribution matches the original and linking the number of cuts to leaf height, extending previous results.
Contribution
It generalizes a known result from Aldous's tree to Le9vy trees, demonstrating the invariance of the tree distribution under a specific pruning-regrafting procedure.
Findings
Regrafted tree has the same distribution as the original Le9vy tree.
Number of cuts needed to isolate the root equals the height of a random leaf.
Generalizes previous results from Aldous's tree to Le9vy trees.
Abstract
We perform a pruning procedure on a L\'evy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the L\'evy tree). We prove that the tree constructed by regrafting is distributed as the original L\'evy tree, generalizing a result where only Aldous's tree is considered. As a consequence, we obtain that the quantity which represents in some sense the number of cuts needed to isolate the root of the tree, is distributed as the height of a leaf picked at random in the L\'evy tree.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Cellular Automata and Applications · advanced mathematical theories
