http://www.bibsonomy.org/burst/user/pitman/asymptotic_lawBibSonomy BuRST Feed for /user/pitman/asymptotic_law2008-09-07T20:10:47+02:00http://www.bibsonomy.org/bibtex/2c47062e77b3418480a9322d65373ab79/pitmanpitman2008-01-21T00:00:55+01:00subordinator Dept_Mathematics_Berkeley random_compositions Dept_Statistics_Berkeley asymptotic_law author_Pitman__Jim <span style="color:#555555;">Alexander <a href="http://www.bibsonomy.org/author/Gnedin">Gnedin</a> und Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> und Marc <a href="http://www.bibsonomy.org/author/Yor">Yor</a> </span><em>Ann. Probab.</em><em>34(2):468--492</em>(<em>2006</em>)Mon Jan 21 00:00:55 CET 2008Ann. Probab.2468--492Asymptotic laws for compositions derived from transformed subordinators342006subordinator Dept_Mathematics_Berkeley random_compositions Dept_Statistics_Berkeley asymptotic_law author_Pitman__Jim A random composition of $n$ appears when the points of a random closed set $\widetilde{\mathcal{R}}\subset[0,1]$ are used to separate into blocks $n$ points sampled from the uniform distribution. We study the number of parts $K_n$ of this composition and other related functionals under the assumption that $\widetilde{\mathcal{R}}=\phi(S_{\bullet})$, where $(S_t,t\geq0)$ is a subordinator and $\phi:[0,\infty]\to[0,1]$ is a diffeomorphism. We derive the asymptotics of $K_n$ when the L\'{e}vy measure of the subordinator is regularly varying at 0 with positive index. Specializing to the case of exponential function $\phi(x)=1-e^{-x}$, we establish a connection between the asymptotics of $K_n$ and the exponential functional of the subordinator.http://www.bibsonomy.org/bibtex/2d200ff3f576ba1877e1acdb98a698eb6/pitmanpitman2008-01-20T22:45:02+01:00author_Pitman__Jim phylogenetics Dept_Statistics_Berkeley Dept_Mathematics_Berkeley continuum_tree asymptotic_law fragmentation <span style="color:#555555;">Benedicte <a href="http://www.bibsonomy.org/author/Haas">Haas</a> und Gregory <a href="http://www.bibsonomy.org/author/Miermont">Miermont</a> und Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> und Matthias <a href="http://www.bibsonomy.org/author/Winkel">Winkel</a> </span>(<em>2006</em>)Sun Jan 20 22:45:02 CET 2008Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models2006author_Pitman__Jim phylogenetics Dept_Statistics_Berkeley Dept_Mathematics_Berkeley continuum_tree asymptotic_law fragmentation Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application we obtain continuum random tree limits of Aldous's beta-splitting models and Ford's alpha models for phylogenetic trees. This confirms in a strong way that the whole trees grow at the same speed as the mean height of a randomly chosen leaf.SpringerLink - Book Chapterhttp://www.bibsonomy.org/bibtex/28bc1c8955c1318984238b9a1780ea0d2/pitmanpitman2008-01-20T21:52:55+01:00Dept_Statistics_Berkeley random_mappings Dept_Mathematics_Berkeley Brownian_bridge asymptotic_law author_Pitman__Jim <span style="color:#555555;">Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> </span><em>Volume1875vonLecture Notes in Mathematics, </em><em>Seite193--206. </em><em>Springer-Verlag, </em>(<em>2006</em>)Sun Jan 20 21:52:55 CET 2008Combinatorial Stochastic Processes193--206Lecture Notes in MathematicsBrownian bridge asymptotics for random mappings18752006Dept_Statistics_Berkeley random_mappings Dept_Mathematics_Berkeley Brownian_bridge asymptotic_law author_Pitman__Jim This chapter reviews Brownian bridge asymptotics for random mappings, first described in 1994 by Aldous and Pitman. The limit distributions as n→∞, of various functionals of a uniformly distributed random mapping from an n element set to itself, are those of correspondingfunctionals of a Brownian bridge. Similar results known to hold for various non-uniform models of random mappings, accordingto a kind of invariance principle. A mapping Mn : [n] → [n] can be identified with its digraph {i → Mn(i), i ∈ [n]}, as in Figure 1.http://www.bibsonomy.org/bibtex/24be2dcebc2684ccd1c2547b02f6c12e2/pitmanpitman2008-01-20T02:39:38+01:00random_trees_and_forests Dept_Mathematics_Berkeley birthday_problem Dept_Statistics_Berkeley asymptotic_law author_Pitman__Jim <span style="color:#555555;">Michael <a href="http://www.bibsonomy.org/author/Camarri">Camarri</a> und Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> </span><em>Electron. J. Probab.</em>(<em>2000</em>)Sun Jan 20 02:39:38 CET 2008Electron. J. Probab.Paper 2, 1-18Limit distributions and random trees derived from the birthday problem with unequal probabilities52000random_trees_and_forests Dept_Mathematics_Berkeley birthday_problem Dept_Statistics_Berkeley asymptotic_law author_Pitman__Jim http://www.bibsonomy.org/bibtex/2fba39187049f51f55844466933b0fafe/pitmanpitman2008-01-20T02:39:38+01:00author_Pitman__Jim Dept_Mathematics_Berkeley asymptotic_law Dept_Statistics_Berkeley path_decomposition conditioned_process <span style="color:#555555;">Michael <a href="http://www.bibsonomy.org/author/Klass">Klass</a> und Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> </span><em>Statistics and Probability Letters</em>(<em>1993</em>)Sun Jan 20 02:39:38 CET 2008Statistics and Probability Letters13-17Limit laws for {B}rownian motion conditioned to reach a high level171993author_Pitman__Jim Dept_Mathematics_Berkeley asymptotic_law Dept_Statistics_Berkeley path_decomposition conditioned_process http://www.bibsonomy.org/bibtex/2f8a71e9cbf7e92e5bb1e783d6ce3c61a/pitmanpitman2008-01-20T02:39:38+01:00Dept_Mathematics_Berkeley Dept_Statistics_Berkeley Brownian_winding asymptotic_law author_Pitman__Jim planar_Brownian_motion <span style="color:#555555;">Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> und Marc <a href="http://www.bibsonomy.org/author/Yor">Yor</a> </span><em>Annals of Probability</em>(<em>1989</em>)Sun Jan 20 02:39:38 CET 2008Annals of Probability965-1011Further asymptotic laws of planar {Brownian} motion171989Dept_Mathematics_Berkeley Dept_Statistics_Berkeley Brownian_winding asymptotic_law author_Pitman__Jim planar_Brownian_motion http://www.bibsonomy.org/bibtex/2a8f3d0b1a1af26ea07419dcddefce5e5/pitmanpitman2008-01-20T02:39:38+01:00author_Pitman__Jim Markov_excursion Markov_crossing Dept_Statistics_Berkeley Dept_Mathematics_Berkeley asymptotic_law <span style="color:#555555;">Krzysztof <a href="http://www.bibsonomy.org/author/Burdzy">Burdzy</a> und Jim W. <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> und Marc <a href="http://www.bibsonomy.org/author/Yor">Yor</a> </span><em>Colloque Paul L\'evy sur les Processus Stochastiques, </em><em>Seite59-74. </em><em>Soci'et'e Math'ematique de France, </em>(<em>1988</em>)Sun Jan 20 02:39:38 CET 2008Colloque Paul L{\'e}vy sur les Processus Stochastiques59-74Ast{\'e}risque 157-158Some Asymptotic Laws for Crossings and Excursions1988author_Pitman__Jim Markov_excursion Markov_crossing Dept_Statistics_Berkeley Dept_Mathematics_Berkeley asymptotic_law http://www.bibsonomy.org/bibtex/2c5d638e6ee992755bfb9ce7561db272d/pitmanpitman2008-01-20T02:39:38+01:00Dept_Mathematics_Berkeley author_Pitman__Jim asymptotic_law planar_Brownian_motion Dept_Statistics_Berkeley Brownian_winding <span style="color:#555555;">Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> und Marc <a href="http://www.bibsonomy.org/author/Yor">Yor</a> </span><em>C.R. Acad. Sc. Paris, S\'erie I</em>(<em>1987</em>)Sun Jan 20 02:39:38 CET 2008C.R. Acad. Sc. Paris, S{\'e}rie I757-760Compl{\'e}ments {\`a} l'{\'e}tude asymptotique des nombres de tours du mouvement brownien complexe autour d'un nombre fini de points3051987Dept_Mathematics_Berkeley author_Pitman__Jim asymptotic_law planar_Brownian_motion Dept_Statistics_Berkeley Brownian_winding http://www.bibsonomy.org/bibtex/2655232e8f90bf9841b09592d1ac98fd7/pitmanpitman2008-01-20T02:39:38+01:00Dept_Statistics_Berkeley author_Pitman__Jim asymptotic_law Brownian_winding planar_Brownian_motion Dept_Mathematics_Berkeley <span style="color:#555555;">Jim <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> und Marc <a href="http://www.bibsonomy.org/author/Yor">Yor</a> </span><em>Annals of Probability</em>(<em>1986</em>)Sun Jan 20 02:39:38 CET 2008Annals of Probability733-779Asymptotic laws of planar {B}rownian motion141986Dept_Statistics_Berkeley author_Pitman__Jim asymptotic_law Brownian_winding planar_Brownian_motion Dept_Mathematics_Berkeley http://www.bibsonomy.org/bibtex/29d48435346dfed817f9e339562b16f2d/pitmanpitman2008-01-20T02:39:38+01:00Dept_Mathematics_Berkeley asymptotic_law author_Pitman__Jim Brownian_winding planar_Brownian_motion Dept_Statistics_Berkeley <span style="color:#555555;">J. W. <a href="http://www.bibsonomy.org/author/Pitman">Pitman</a> und M. <a href="http://www.bibsonomy.org/author/Yor">Yor</a> </span><em>Bulletin of the American Mathematical Society</em>(<em>1984</em>)Sun Jan 20 02:39:38 CET 2008Bulletin of the American Mathematical Society109-111The asymptotic joint distribution of windings of planar {B}rownian motion101984Dept_Mathematics_Berkeley asymptotic_law author_Pitman__Jim Brownian_winding planar_Brownian_motion Dept_Statistics_Berkeley