Brownian Bridge Asymptotics for Random p-Mappings
David Aldous, University of California, Berkeley
Gregory Miermont, Ecole Normale Superieure
Jim Pitman, University of California, Berkeley
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 Aldous-Pitman (1994) result on convergence of uniform random
mapping walks to reflecting Brownian bridge,
and extend this result to random p-mappings.
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