Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Random permutations and unique fully supported ergodicity for the Euler adic transformation

Sarah Bailey Frick and Karl Petersen

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Abstract

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.

Résumé

Pour la transformation adique sur l’espace des chemins infinis dans le graphe associé aux nombres Euleriens, il n’existe qu’une seule mesure de probabilité ergodique invariante avec support total. Ce résultat peut justifier en partie une hypothèse fréquente sur l’équidistribution des permutations aléatoires.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist. Volume 44, Number 5 (2008), 876-885.

Dates
First available: 24 September 2008

Permanent link to this document
http://projecteuclid.org/euclid.aihp/1222261916

Digital Object Identifier
doi:10.1214/07-AIHP133

Zentralblatt MATH identifier
05611465

Mathematical Reviews number (MathSciNet)
MR2453848

Subjects
Primary: 37A05: Measure-preserving transformations 37A25: Ergodicity, mixing, rates of mixing 37A50: Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 37B99: None of the above, but in this section 60B05: Probability measures on topological spaces 62F07: Ranking and selection

Keywords
Random permutations Eulerian numbers Adic transformation Invariant measures Ergodic transformations Bratteli diagrams Rises and falls

Citation

Frick, Sarah Bailey; Petersen, Karl. Random permutations and unique fully supported ergodicity for the Euler adic transformation. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 44 (2008), no. 5, 876--885. doi:10.1214/07-AIHP133. http://projecteuclid.org/euclid.aihp/1222261916.


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References

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