Electronic Journal of Probability

Brownian Bridge Asymptotics for Random $p$-Mappings

David Aldous, Gregory Miermont, and Jim Pitman

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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.

Article information

Electron. J. Probab., Volume 9 (2004), paper no. 3, 37-56.

Accepted: 10 December 2003
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability
Secondary: 60F17: Functional limit theorems; invariance principles 60J65: Brownian motion [See also 58J65]

Brownian bridge Brownian excursion Joyal map random mapping random tree weak convergence

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Aldous, David; Miermont, Gregory; Pitman, Jim. Brownian Bridge Asymptotics for Random $p$-Mappings. Electron. J. Probab. 9 (2004), paper no. 3, 37--56. doi:10.1214/EJP.v9-186. https://projecteuclid.org/euclid.ejp/1465229689

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