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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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