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from Part II - Results and Applications
Published online by Cambridge University Press: 16 May 2024
This chapter provides a full elementary proof of Gromov’s theorem, which states that a finitely generated group has polynomial growth if and only if it is virtually nilpotent. The proof proceeds along the ideas laid forth by Ozawa, using the existence of a harmonic cocycle. Gromov’s theorem is then used to classify all recurrent groups. Also, consequences of harmonic cocycle to diffusivitiy of the walk are shown.
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