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Brownian bridge asymptotics for random $$p$$-mappings. (English) Zbl 1064.60012
Summary: The Joyal bijection between doubly-rooted trees and mappings can be lifted to a transformation on function space which takes tree-walks to mappings-walks. Applying known results on weak convergence of random tree walks to Brownian excursion, we give a conceptually simpler rederivation of the result of D. J. Aldous and J. Pitman [Random Struct. Algorithms 5, No. 4, 487–512 (1994; Zbl 0811.60057)] on convergence of uniform random mapping walks to reflecting Brownian bridge, and extend this result to random $${\mathbf p}$$-mappings.

MSC:
 60C05 Combinatorial probability 60F17 Functional limit theorems; invariance principles 60J65 Brownian motion
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