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Random divergence of groups
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The divergence of a group is a quasi-isometry invariant defined in terms of pairs of points and lengths of paths avoiding a suitable ball around the identity. In this paper we study "random divergence'', meaning the divergence at two points chosen according to independent random walks or Markov chains; the Markov chains version can be turned into a quasi-isometry invariant. We show that in many cases, such as for relatively hyperbolic groups, mapping class groups, and right-angled Artin groups, the divergence at two randomly chosen points is with high probability equivalent to the divergence of the group. That is, generic points realise the largest possible divergence.
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Cited by 1 Pith paper
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Growth gaps and exponential genericity in acylindrically hyperbolic groups
WPD elements are exponentially generic for every finite generating set of an acylindrically hyperbolic group, yielding growth tightness and cogrowth tightness.
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