%0 Journal Article %1 amp03 %A Aldous, D. J. %A Miermont, G. %A Pitman, J. %D 2004 %J Probab. Theory Related Fields %K Dept_Mathematics_Berkeley Dept_Statistics_Berkeley continuum_tree exploration_process identities_in_law local_time myown %N 2 %P 182--218 %T The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin's local time identity %V 129 %X We study the inhomogeneous continuum random trees (ICRT) that arise as weak limits of birthday trees. We give a description of the exploration process, a function defined on 0,1 that encodes the structure of an ICRT, and also of its width process, determining the size of layers in order of height. These processes turn out to be transformations of bridges with exchangeable increments, which have already appeared in other ICRT related topics such as stochastic additive coalescence. The results rely on two different constructions of birthday trees from processes with exchangeable increments, on weak convergence arguments, and on general theory on continuum random trees.

@article{amp03, abstract = { We study the inhomogeneous continuum random trees (ICRT) that arise as weak limits of birthday trees. We give a description of the exploration process, a function defined on [0,1] that encodes the structure of an ICRT, and also of its width process, determining the size of layers in order of height. These processes turn out to be transformations of bridges with exchangeable increments, which have already appeared in other ICRT related topics such as stochastic additive coalescence. The results rely on two different constructions of birthday trees from processes with exchangeable increments, on weak convergence arguments, and on general theory on continuum random trees. }, added-at = {2008-01-21T00:15:39.000+0100}, arxiv = {math.PR/0403137}, author = {Aldous, D. J. and Miermont, G. and Pitman, J.}, bibnumber = {zzz}, biburl = {https://www.bibsonomy.org/bibtex/2deb0b1d3fcc749242d2539648f78fa9f/pitman}, coden = {PTRFEU}, fjournal = {Probability Theory and Related Fields}, id_ucb-stat = {643}, institution = {Dept. Statistics, U.C. Berkeley}, interhash = {43a2af4a390b6b7b7536b1586fb15fb1}, intrahash = {deb0b1d3fcc749242d2539648f78fa9f}, issn = {0178-8051}, journal = {Probab. Theory Related Fields}, keywords = {Dept_Mathematics_Berkeley Dept_Statistics_Berkeley continuum_tree exploration_process identities_in_law local_time myown}, mrclass = {60C05 (60F17 60G09 60G51)}, mrnumber = {MR2063375}, number = 2, pages = {182--218}, timestamp = {2010-10-30T22:51:58.000+0200}, title = {{The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin's local time identity}}, urls = {http://springerlink.com/link.asp?id=p5xwbxbujy2gd6up [Springer]}, volume = 129, xurlpdf = {http://stat.berkeley.edu/users/aldous/640.pdf}, xurlpsz = {http://stat.berkeley.edu/tech-reports/640.ps.Z}, year = 2004 }