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math.GR2014★ 2 cited
Non-Liouville groups with return probability exponent at most 1/2
Michał Kotowski, Bálint Virág
We construct a finitely generated group without the Liouville property such that the return probability of a random walk satisfies . Re…
math.GR2011★ 23 cited
Random groups and Property (T): Żuk's theorem revisited
Marcin Kotowski, Michal Kotowski
We provide a full and rigorous proof of a theorem attributed to Żuk, stating that random groups in the Gromov density model for d > 1/3 have property (T) with high probability. The…