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Article Dans Une Revue Annals of Mathematics Année : 2021

Speed of random walks, isoperimetry and compression of finitely generated groups

Tianyi Zheng
  • Fonction : Auteur

Résumé

We give a solution to the inverse problem (given a function, find a corresponding group) for large classes of speed, entropy, isoperimetric profile, return probability and $L_p$-compression functions of finitely generated groups of exponential volume growth. For smaller classes, we give solutions among solvable groups. As corollaries, we prove a recent conjecture of Amir on joint evaluation of speed and entropy exponents and we obtain a new proof of the existence of uncountably many pairwise non-quasi-isometric solvable groups, originally due to Cornulier and Tessera. We also obtain a formula relating the $L_p$-compression exponent of a group and its wreath product with the cyclic group for $p$ in $[1,2]$.
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Dates et versions

hal-02048188 , version 1 (04-04-2024)

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Jérémie Brieussel, Tianyi Zheng. Speed of random walks, isoperimetry and compression of finitely generated groups. Annals of Mathematics, 2021, 193 (1), ⟨10.4007/annals.2021.193.1.1⟩. ⟨hal-02048188⟩
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