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.
Publié le : 2008-10-15
Classification:
Random permutations,
Eulerian numbers,
Adic transformation,
Invariant measures,
Ergodic transformations,
Bratteli diagrams,
Rises and falls,
37A05,
37A25,
37A50,
37B99,
60B05,
62F07
@article{1222261916,
author = {Frick, Sarah Bailey and Petersen, Karl},
title = {Random permutations and unique fully supported ergodicity for the Euler adic transformation},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 876-885},
language = {en},
url = {http://dml.mathdoc.fr/item/1222261916}
}
Frick, Sarah Bailey; Petersen, Karl. Random permutations and unique fully supported ergodicity for the Euler adic transformation. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 876-885. http://gdmltest.u-ga.fr/item/1222261916/