Aldous, David; Miermont, Grégory; Pitman, Jim Brownian bridge asymptotics for random \(p\)-mappings. (English) Zbl 1064.60012 Electron. J. Probab. 9, Paper No. 3, 37-56 (2004). 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. Cited in 11 Documents MathOverflow Questions: Brownian bridge interpreted as Brownian motion on the circle MSC: 60C05 Combinatorial probability 60F17 Functional limit theorems; invariance principles 60J65 Brownian motion Keywords:Brownian bridge; Brownian excursion; Joyal map; random mapping; random tree; weak convergence Citations:Zbl 0811.60057 PDFBibTeX XMLCite \textit{D. Aldous} et al., Electron. J. Probab. 9, Paper No. 3, 37--56 (2004; Zbl 1064.60012) Full Text: DOI EuDML EMIS