Abstract
This chapter reviews Brownian bridge asymptotics for random mappings, first described in 1994 by Aldous and Pitman. The limit distributions as n→∞, of various functionals of a uniformly distributed random mapping from an n element set to itself, are those of corresponding functionals of a Brownian bridge. Similar results known to hold for various non-uniform models of random mappings, according to a kind of invariance principle. A mapping M n : [n] → [n] can be identified with its digraph {i → M n (i), i ∈ [n]}, as in Figure 1.
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© 2006 Springer-Verlag Berlin/Heidelberg
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Pitman, J. (2006). Brownian bridge asymptotics for random mappings. In: Picard, J. (eds) Combinatorial Stochastic Processes. Lecture Notes in Mathematics, vol 1875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34266-4_10
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DOI: https://doi.org/10.1007/3-540-34266-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30990-1
Online ISBN: 978-3-540-34266-3
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