%0 Book Section %1 csp-map %A Pitman, Jim %B Combinatorial Stochastic Processes %D 2006 %I Springer-Verlag %K Brownian_bridge Dept_Mathematics_Berkeley Dept_Statistics_Berkeley asymptotic_law random_mappings myown %P 193--206 %T Brownian bridge asymptotics for random mappings %U http://dx.doi.org/10.1007/3-540-34266-4_10 %V 1875 %X 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 correspondingfunctionals of a Brownian bridge. Similar results known to hold for various non-uniform models of random mappings, accordingto a kind of invariance principle. A mapping Mn : n → n can be identified with its digraph i → Mn(i), i ∈ n, as in Figure 1.

@inbook{csp-map, 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 correspondingfunctionals of a Brownian bridge. Similar results known to hold for various non-uniform models of random mappings, accordingto a kind of invariance principle. A mapping Mn : [n] → [n] can be identified with its digraph {i → Mn(i), i ∈ [n]}, as in Figure 1.}, added-at = {2008-01-20T21:52:55.000+0100}, author = {Pitman, Jim}, biburl = {https://www.bibsonomy.org/bibtex/28bc1c8955c1318984238b9a1780ea0d2/pitman}, booktitle = {Combinatorial Stochastic Processes}, description = {SpringerLink - Book Chapter}, interhash = {506c5c39e62a37ea62e96324d5ff2c62}, intrahash = {8bc1c8955c1318984238b9a1780ea0d2}, keywords = {Brownian_bridge Dept_Mathematics_Berkeley Dept_Statistics_Berkeley asymptotic_law random_mappings myown}, pages = {193--206}, publisher = {Springer-Verlag}, series = {Lecture Notes in Mathematics}, timestamp = {2010-10-30T22:51:58.000+0200}, title = {Brownian bridge asymptotics for random mappings}, url = {http://dx.doi.org/10.1007/3-540-34266-4_10}, volume = 1875, year = 2006 }