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 Electronic Journal of Probability > Vol. 9 (2004) > Paper 3 open journal systems 


Brownian Bridge Asymptotics for Random p-Mappings

David Aldous, University of California, Berkeley
Gregory Miermont, Ecole Normale Superieure
Jim Pitman, University of California, Berkeley


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.


Full text: PDF

Pages: 37-56

Published on: February 13, 2004
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Electronic Journal of Probability. ISSN: 1083-6489