Random permutations and unique fully supported ergodicity for the Euler adic transformation
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 5, p. 876-885

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.

DOI : https://doi.org/10.1214/07-AIHP133
Classification:  37A05,  37A25,  37A50,  37B99,  60B05,  62F07
Keywords: random permutations, eulerian numbers, adic transformation, invariant measures, ergodic transformations, Bratteli diagrams, rises and falls
@article{AIHPB_2008__44_5_876_0,
     author = {Frick, Sarah Bailey and Petersen, Karl},
     title = {Random permutations and unique fully supported ergodicity for the Euler adic transformation},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {5},
     year = {2008},
     pages = {876-885},
     doi = {10.1214/07-AIHP133},
     zbl = {1175.37005},
     mrnumber = {2453848},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2008__44_5_876_0}
}
Frick, Sarah Bailey; Petersen, Karl. Random permutations and unique fully supported ergodicity for the Euler adic transformation. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 5, pp. 876-885. doi : 10.1214/07-AIHP133. http://www.numdam.org/item/AIHPB_2008__44_5_876_0/

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