Geodesic
On the joint behaviour of speed and entropy of random walks on groups
Gideon Amir1 orcid
1Bar-Ilan University, Ramat Gan, Israel
Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 455-467

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DOI

For every 3/4≤δ,β<1 satisfying δ≤β<21+δ​ we construct a finitely generated group Γ and a (symmetric, finitely supported) random walk Xn​ on Γ so that its expected distance from its starting point satisfies E∣Xn​∣≍nβ and its entropy satisfies H(Xn​)≍nδ. In fact, the speed and entropy can be set precisely to equal any two nice enough prescribed functions f,h up to a constant factor as long as the functions satisfy the relation n43​≤h(n)≤f(n)≤nh(n)/log(n+1)​≤nγ for some γ<1.
DOI : 10.4171/ggd/403
Classification : 05-XX, 20-XX, 60-XX
Mots-clés : Random walk, groups, entropy, rate of escape, permutation wreath product, automaton groups

Gideon Amir  1

1 Bar-Ilan University, Ramat Gan, Israel 
Gideon Amir. On the joint behaviour of speed and entropy of random walks on groups. Groups, geometry, and dynamics, Tome 11 (2017) no. 2, pp. 455-467. doi: 10.4171/ggd/403
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     pages = {455--467},
     year = {2017},
     volume = {11},
     number = {2},
     doi = {10.4171/ggd/403},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/403/}
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