Brownian bridge asymptotics for random p-mappings
- Author(s): Aldous, D
- Miermont, G
- Pitman, J
- et al.
Published Web Locationhttps://doi.org/10.1214/EJP.v9-186
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.