%0 Generic %1 hpw07 %A Haas, Bénédicte %A Pitman, Jim %A Winkel, Matthias %D 2007 %K Dept_Mathematics_Berkeley Dept_Statistics_Berkeley continuum_random_tree invariance_under_re-rooting random_trees_and_forests spinal_partition myown %T Spinal partitions and invariance under re-rooting of continuum random trees %X We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second application of spinal decompositions, we prove that among the continuous fragmentation trees, stable trees are the only ones whose distribution is invariant under uniform re-rooting.

@misc{hpw07, abstract = {We develop some theory of spinal decompositions of discrete and continuous fragmentation trees. Specifically, we consider a coarse and a fine spinal integer partition derived from spinal tree decompositions. We prove that for a two-parameter Poisson-Dirichlet family of continuous fragmentation trees, including the stable trees of Duquesne and Le Gall, the fine partition is obtained from the coarse one by shattering each of its parts independently, according to the same law. As a second application of spinal decompositions, we prove that among the continuous fragmentation trees, stable trees are the only ones whose distribution is invariant under uniform re-rooting.}, added-at = {2008-01-20T22:54:17.000+0100}, arxiv = {0705.3602}, author = {Haas, Bénédicte and Pitman, Jim and Winkel, Matthias}, biburl = {https://www.bibsonomy.org/bibtex/25e0f11ddcbf7d5a422864240aa1b7861/pitman}, interhash = {db1337bfb69f400216ad4f3605816e92}, intrahash = {5e0f11ddcbf7d5a422864240aa1b7861}, keywords = {Dept_Mathematics_Berkeley Dept_Statistics_Berkeley continuum_random_tree invariance_under_re-rooting random_trees_and_forests spinal_partition myown}, timestamp = {2010-10-30T22:51:58.000+0200}, title = {Spinal partitions and invariance under re-rooting of continuum random trees}, year = 2007 }