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Article Dans Une Revue Israel Journal of Mathematics Année : 2019

No iterated identities satisfied by all finite groups

Alexei Belov
  • Fonction : Auteur

Résumé

Abstract We prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite $$(2+\epsilon )$$ ( 2 + ϵ ) -moment. This result is in contrast with classical examples of abelian groups, where the displacement after n steps, normalised by its mean, does not concentrate, and the limiting distribution of the normalised n -step displacement admits a density whose support is $$[0,\infty )$$ [ 0 , ∞ ) . We study further examples of groups, some with random walks satisfying LLN for drift and other examples where such concentration phenomenon does not hold, and study relation of this property with asymptotic geometry of groups.

Dates et versions

hal-03958771 , version 1 (26-01-2023)

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Alexei Belov, Anna Erschler. No iterated identities satisfied by all finite groups. Israel Journal of Mathematics, 2019, 233 (1), pp.167-197. ⟨10.1007/s11856-019-1904-4⟩. ⟨hal-03958771⟩
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