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Statistical hyperbolicity of relatively hyperbolic groups

Jeremy Osborne and Wen-yuan Yang

Algebraic & Geometric Topology 16 (2016) 2143–2158

We prove that a nonelementary relatively hyperbolic group is statistically hyperbolic with respect to every finite generating set. We also establish the statistical hyperbolicity for certain direct products of two groups, one of which is relatively hyperbolic.

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Relatively hyperbolic groups, Statistical hyperbolicity, Growth function
Mathematical Subject Classification 2010
Primary: 20F65, 20F67
Received: 30 April 2015
Revised: 8 September 2015
Accepted: 30 September 2015
Published: 12 September 2016
Jeremy Osborne
University of Wisconsin
Mathematics and Physics Department
Kenosha, WI 53144
United States
Wen-yuan Yang
Beijing International Center for Mathematical Research & School of Mathematical Sciences
Peking University
Beijing, 100871