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The Hausdorff measure of stable trees. (English) Zbl 1128.60072
Authors’ abstract: 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.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G17 Sample path properties
60G52 Stable stochastic processes
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