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Brownian Bridge Asymptotics for Random $p$-Mappings

   
@article{EJP186,
	author = {David Aldous and Gregory Miermont and Jim Pitman},
	title = {Brownian Bridge Asymptotics for Random $p$-Mappings},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {9},
	year = {2004},
	keywords = {Brownian bridge, Brownian excursion, Joyal map, random mapping, random tree, weak convergence.},
	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.},
	pages = {no. 3, 37-56},
	issn = {1083-6489},
	doi = {10.1214/EJP.v9-186},    
        url = {http://ejp.ejpecp.org/article/view/186}}