The Joyal bijection between doubly-rooted trees and mappings can be lifted to a transformation on function space which takes tree-walks to mapping-walks. Applying known results on weak convergence of random tree walks to Brownian excursion, we give a conceptually simpler rederivation of the Aldous-Pitman (1994) result on convergence of uniform random mapping walks to reflecting Brownian bridge, and extend this result to random p-mappings.
%0 Journal Article
%1 amp02
%A Aldous, D. J.
%A Miermont, G.
%A Pitman, J.
%D 2004
%J Electron. J. Probab.
%K Brownian_bridge Dept_Mathematics_Berkeley Dept_Statistics_Berkeley combinatorial_stochastic_process random_mappings myown
%P 37--56
%T Brownian bridge asymptotics for random p-mappings
%U http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1429&layout=abstract
%V 9
%X The Joyal bijection between doubly-rooted trees and mappings can be lifted to a transformation on function space which takes tree-walks to mapping-walks. Applying known results on weak convergence of random tree walks to Brownian excursion, we give a conceptually simpler rederivation of the Aldous-Pitman (1994) result on convergence of uniform random mapping walks to reflecting Brownian bridge, and extend this result to random p-mappings.
@article{amp02,
abstract = {The Joyal bijection between doubly-rooted trees and mappings can be lifted to a transformation on function space which takes tree-walks to mapping-walks. Applying known results on weak convergence of random tree walks to Brownian excursion, we give a conceptually simpler rederivation of the Aldous-Pitman (1994) result on convergence of uniform random mapping walks to reflecting Brownian bridge, and extend this result to random p-mappings.},
added-at = {2008-01-20T02:39:38.000+0100},
author = {Aldous, D. J. and Miermont, G. and Pitman, J.},
bibnumber = {119},
biburl = {https://www.bibsonomy.org/bibtex/25201a7379b7c60468265c8da2c8d4f2f/pitman},
id_ucb-stat = {624},
interhash = {ed8359f844d78f4d780bdb88bfc7fe20},
intrahash = {5201a7379b7c60468265c8da2c8d4f2f},
journal = {Electron. J. Probab.},
keywords = {Brownian_bridge Dept_Mathematics_Berkeley Dept_Statistics_Berkeley combinatorial_stochastic_process random_mappings myown},
mrnumber = {MR2041828},
pages = {37--56},
timestamp = {2010-10-30T22:51:57.000+0200},
title = {Brownian bridge asymptotics for random {\em p}-mappings},
url = {http://www.math.washington.edu/~ejpecp/viewarticle.php?id=1429&layout=abstract},
volume = 9,
year = 2004
}