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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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.


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.

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

First available in Project Euclid: 24 September 2008

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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

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


Frick, Sarah Bailey; Petersen, Karl. Random permutations and unique fully supported ergodicity for the Euler adic transformation. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 5, 876--885. doi:10.1214/07-AIHP133.

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