Geodesic
Amenability of linear-activity automaton groups
Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 705-730 Cet article a éte moissonné depuis la source EMS Press

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We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
DOI : 10.4171/jems/373
Classification : 60-XX, 20-XX, 00-XX
Keywords: amenability, automaton groups, self-similar, random walk, entropy 
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     author = {Gideon Amir and Omer Angel and B\'alint Vir\'ag},
     title = {Amenability of linear-activity automaton groups},
     journal = {Journal of the European Mathematical Society},
     pages = {705--730},
     year = {2013},
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     doi = {10.4171/jems/373},
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Gideon Amir; Omer Angel; Bálint Virág. Amenability of linear-activity automaton groups. Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 705-730. doi: 10.4171/jems/373

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