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The quantile rearrangement of random walk increments
Probability| Speaker: | Noah Forman, UC Berkeley |
| Location: | 1147 MSB |
| Start time: | Wed, Dec 5 2012, 4:10PM |
Description
From a simple random walk one may obtain a random permutation of
indices [1,n] via the lexicographic ordering first on the value of the walk
at a given time, and second by the time itself. We demonstrate that by
rearranging the increments of a random walk bridge according to this
quantile permutation, we obtain a Dyck path. Passing to a Brownian limit
gives a novel proof and a generalization of a theorem of Jeulin (1985)
concerning Brownian local times.