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Article
Brownian bridge asymptotics for random mappings
Article first published online: 11 OCT 2006
DOI: 10.1002/rsa.3240050402
Copyright © 1994 Wiley Periodicals, Inc., A Wiley Company
1098-2418/asset/cover.gif?v=1&s=8c37a8c420571f9d82e3fc7c4b0d96e07641b77f "Random Structures & Algorithms")
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How to Cite
Aldous, D. J. and Pitman, J. (1994), Brownian bridge asymptotics for random mappings. Random Struct. Alg., 5: 487–512. doi: 10.1002/rsa.3240050402
Publication History
- Issue published online: 11 OCT 2006
- Article first published online: 11 OCT 2006
- Manuscript Accepted: 7 OCT 1993
- Manuscript Revised: 10 AUG 1993
- Manuscript Received: 5 AUG 1992
Funded by
- NSF. Grant Number: DMS90-01710, DMS91-07531
- Abstract
- References
- Cited By
Abstract
Uniform random mappings of an n-element set to itself have been much studied in the combinatorial literature. We introduce a new technique, which starts by specifying a coding of mappings as walks with ± 1 steps. The uniform random mapping is thereby coded as a nonuniform random walk, and our main result is that as n→∞ the random walk rescales to reflecting Brownian bridge. This result encompasses a large number of limit theorems for “global” characteristics of uniform random mappings. © 1994 John Wiley & Sons, Inc.