Geodesic
Random orderings and unique ergodicity of automorphism groups
Journal of the European Mathematical Society, Tome 16 (2014) no. 10, pp. 2059-2095.

Voir la notice de l'article provenant de la source EMS Press

We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations of the integers. We also contrast these results to those for certain special classes of graphs and metric spaces in which such random orderings can be found that are not uniform.
DOI : 10.4171/jems/483
Classification : 22-XX, 03-XX, 28-XX, 37-XX
Keywords: Graphs, hypergraphs, the random graph, metric spaces, Fraïssé, Ramsey, minimal flow, Urysohn space 
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     title = {Random orderings and unique ergodicity of automorphism groups},
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Omer Angel; Alexander S. Kechris; Russell Lyons. Random orderings and unique ergodicity of automorphism groups. Journal of the European Mathematical Society, Tome 16 (2014) no. 10, pp. 2059-2095. doi : 10.4171/jems/483. http://geodesic.mathdoc.fr/articles/10.4171/jems/483/

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