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Abstract: Aldous and Pitman (1994) studied asymptotic distributions as n -> \infty, of various functionals of a uniform random mapping of the set {1, ..., n}, by constructing a mapping-walk and showing these random walks converge weakly to a reflecting Brownian bridge. Two different ways to encode a mapping as a walk lead to two different decompositions of the Brownian bridge, each defined by cutting the path of the bridge at an increasing sequence of recursively defined random times in the zero set of... (Update)
Context of citations to this paper: More
...context. In the Brownian bridge limit setting of Theorem 1, these lead to different recursive decompositions of Brownian bridge, discussed in detail in [1]. In the following figure, we draw a tree with a spine (ffl vertices) and we run a p sample on it. The crosses...
...for the p mapping model of [14, 17] and that proofs can be simplified by use of Joyal s bijection between mappings and trees. In [3] we develop a variety of distributional results dealing with the decomposition of Brownian bridge at the times D V (j) and with an...
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Invariance Principles for Non-uniform Random Mappings and Trees - Aldous, Pitman (2001) (Correct)
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The Asymptotic Distribution of the Diameter of a Random Mapping - Aldous, Pitman (2002) (Correct)
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1.1: Brownian Bridge Asymptotics for Random p-Mappings - Aldous, Miermont, Pitman (2002) (Correct)
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BibTeX entry: (Update)
D. J. Aldous and J. Pitman. Two recursive decompositions of Brownian bridge related to the asymptotics of random mappings. Technical Report 595, Dept. Statistics, U.C. Berkeley, 2002. http://citeseer.ist.psu.edu/aldous02two.html More
@techreport{ aldous02two,
author = "D. Aldous and J. Pitman",
title = "Two recursive decompositions of Brownian bridge related to the asymptotics
of random mappings",
number = "595",
institution = "Dept. Statistics, U.C. Berkeley",
year = "2002",
url = "citeseer.ist.psu.edu/aldous02two.html" }
Citations (may not include all citations):234 Continuous martingales and Brownian motion (context) - Revuz, Yor - 1999
51 The continuum random tree III (context) - Aldous - 1993
50 Adventures in Stochastic Processes (context) - Resnick - 1992
43 Diffusion Processes and their Sample Paths (context) - Ito, McKean - 1965
42 The two-parameter Poisson-Dirichlet distribution derived fro.. - Pitman, Yor - 1997
38 Poisson Processes (context) - Kingman - 1993
35 Brownian bridge asymptotics for random mappings (context) - Aldous, Pitman - 1994
32 Arcsine laws and interval partitions derived from a stable s.. (context) - Pitman, Yor - 1992
26 Path transformations connecting Brownian bridge (context) - Bertoin, Pitman - 1994
26 Size-biased sampling of Poisson point processes and excursio.. (context) - Perman, Pitman et al. - 1992
24 Random discrete distributions (context) - Kingman - 1975
18 The SDE solved by local times of a Brownian excursion or bri.. - Pitman - 1999
15 Partition structures derived from Brownian motion and stable.. - Pitman - 1997
12 Un processus qui ressemble au pont brownien (context) - Biane, Le Gall et al. - 1987
12 Probability laws related to the Jacobi theta and Riemann zet.. - Biane, Pitman et al. - 2001
11 II: Ito Calculus (context) - Rogers, Williams et al. - 1987
11 Combinatorial Stochastic Processes - Pitman - 2002
9 A model for the distribution of individuals by species in an.. (context) - McCloskey - 1965
9 The law of the maximum of a Bessel bridge - Pitman, Yor - 1999
9 Some developments of the Blackwell-MacQueen urn scheme - Pitman - 1996
8 Markovian bridges: construction (context) - Fitzsimmons, Pitman et al. - 1992
8 Une extension multidimensionnelle de la loi de l'arc sinus (context) - Barlow, Pitman et al. - 1989
8 Fluctuation identities for L'evy processes and splitting at .. (context) - Greenwood, Pitman - 1980
8 Sur certains processus stochastiques homog`enes (context) - L'evy - 1939
7 On Walsh's Brownian motions (context) - Barlow, Pitman et al. - 1989
7 Random Brownian scaling identities and splicing of Bessel pr.. - Pitman, Yor - 1998
6 and maxima for Brownian motion (context) - Knight, times et al. - 1988
5 Cambridge Tracts in Math (context) - Bertoin, Cambridge - 1996
5 forests and subsets associated with Abel-Cayley-Hurwitz mult.. (context) - Pitman - 2001
5 The depth first processes of GaltonWatson trees converge to .. (context) - Marckert, Mokkadem - 2001
5 Generalized arc-sine laws for one-dimensional diffusion proc.. (context) - Watanabe - 1995
4 volume 65 of Translations of Mathematical Monographs (context) - Zolotarev, distributions - 1986
4 Limit measures arising in the theory of groups (context) - Vershik, Shmidt - 1977
4 Invariance principles for non-uniform random mappings and tr.. - Aldous, Pitman - 2001
4 the distribution of ranked heights of excursions of a Browni.. - Pitman, Yor - 2001
4 Nonuniform random transformations (context) - O'Cinneide, Pokrovskii - 2000
3 Brownian bridge asymptotics for random mappings (context) - Biane, on - 1994
2 Brownian bridge asymptotics for random p-mappings - Aldous, Miermont et al. - 2002
2 The asymptotic distribution of the diameter of a random mapp.. - Aldous, Pitman - 2002
2 The local time intensity of an exchangeable interval partiti.. (context) - Kallenberg - 1983
2 Stable distributions and their applications (context) - Uchaikin, Zolotarev et al. - 1999
2 eme de Ray-Knight `a temps fixe (context) - Leuridan - 1998
2 as a Laplace integral (context) - Pollard, of - 1946
2 the representation of the densities of stable laws by specia.. (context) - Zolotarev - 1994
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