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The uniform random mapping is thereby coded as a nonuniform random walk, and our main result is that as <jats:italic>n<\/jats:italic>\u2192\u221e the random walk rescales to reflecting Brownian bridge. This result encompasses a large number of limit theorems for \u201cglobal\u201d characteristics of uniform random mappings. \u00a9 1994 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/rsa.3240050402","type":"journal-article","created":{"date-parts":[[2007,6,1]],"date-time":"2007-06-01T22:51:15Z","timestamp":1180738275000},"page":"487-512","source":"Crossref","is-referenced-by-count":45,"title":["Brownian bridge asymptotics for random mappings"],"prefix":"10.1002","volume":"5","author":[{"given":"David J.","family":"Aldous","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jim","family":"Pitman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","series-title":"Lecture Notes in Mathematics 1117","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BFb0099420","volume-title":"\u00c9cole d'\u00c9t\u00e9 St. Flour 1983","author":"Aldous D. 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