%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 }