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Brownian Bridge Asymptotics for Random $p$-Mappings
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https://doi.org/10.1214/ejp.v9-186Abstract
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. © 2004 Applied Probability Trust.
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