The Hausdorff measure of stable trees

Details The Hausdorff measure of stable trees The Hausdorff measure of stable trees

2005-09-29

arxiv.org/abs/math/0509690v1

Mathematics

Probability

25 pages

Scientific paper

We study fine properties of the so-called stable trees, which are the scaling limits of critical Galton-Watson trees conditioned to be large. In particular we derive the exact Hausdorff measure function for Aldous' continuum random tree and for its level sets. It follows that both the uniform measure on the tree and the local time measure on a level set coincide with certain Hausdorff measures. Slightly less precise results are obtained for the Hausdorff measure of general stable trees.

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