Abstract

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 1994 Aldous-Pitman result on convergence of uniform random mapping walks to reflecting Brownian bridge, and extend this result to random p-mappings.

Citations