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

• 成果类型: Article
• 署名作者: Brieussel, Jeremie; Zheng, Tianyi
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.193.1.1
• 发表日期: 2021
• 页码: 1-105
• 关键词: coarse differentiation; uniform embeddings; MARKOV-PROCESSES; amenable-groups; distortion; RIGIDITY; hilbert; GROWTH; entropy; THEOREM

摘要

We give a solution to the inverse problem (given a prescribed function, find a corresponding group) for large classes of speed, entropy, isoperimetric profile, return probability and L-p-compression functions of finitely generated groups. For smaller classes, we give solutions among solvable groups of exponential volume growth. 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].