https://hal.inria.fr/hal-01184033Hwang, Hsien-KueiHsien-KueiHwangSTAT Sinica - Institute of Statistical Science - Academia SinicaProfiles of random trees: plane-oriented recursive treesHAL CCSD2005random binary treesPlane-oriented recursive treesprofile of treeslimit distributionconvergence of all momentstotal path length[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS][INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG][INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]Episciences Iam, CoordinationConrado MartÃnez2015-08-12 15:51:572018-01-24 10:46:022015-08-13 09:55:38enConference papershttps://hal.inria.fr/hal-01184033/document10.46298/dmtcs.3361application/pdf1We summarize several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximations of the expected width and the correlation coefficients of two level sizes. We also unveil an unexpected connection between the profile of plane-oriented recursive trees (with logarithmic height) and that of random binary trees (with height proportional to the square root of tree size).