A stationary random graph of no growth rate
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 4, p. 1161-1164

We present a random automorphism-invariant subgraph of a Cayley graph such that with probability 1 its exponential growth rate does not exist.

Nous construisons un sous-graphe aléatoire invariant par automorphismes d'un groupe de Cayley qui n'a presque sûrement pas un taux de croissance exponentiel bien défini.

DOI : https://doi.org/10.1214/13-AIHP563
Classification:  60C05,  05C80
Keywords: unimodular graph, stationary random graph, growth rate
@article{AIHPB_2014__50_4_1161_0,
     author = {Tim\'ar, \'Ad\'am},
     title = {A stationary random graph of no growth rate},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {4},
     year = {2014},
     pages = {1161-1164},
     doi = {10.1214/13-AIHP563},
     zbl = {1303.60014},
     mrnumber = {3269989},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_4_1161_0}
}
Timár, Ádám. A stationary random graph of no growth rate. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 4, pp. 1161-1164. doi : 10.1214/13-AIHP563. http://www.numdam.org/item/AIHPB_2014__50_4_1161_0/

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