A SHARPER THRESHOLD FOR RANDOM GROUPS AT DENSITY ONE-HALF

@article{Duchin2014AST,
  title={A SHARPER THRESHOLD FOR RANDOM GROUPS AT DENSITY ONE-HALF},
  author={Moon Duchin and Kasia Jankiewicz and Shelby C. Kilmer and Samuel Leli{\`e}vre and John M. Mackay and Andrew P. S'anchez},
  journal={Groups, Geometry, and Dynamics},
  year={2014},
  volume={10},
  pages={985-1005}
}
  • Moon Duchin, Kasia Jankiewicz, +3 authors Andrew P. S'anchez
  • Published 2014
  • Mathematics
  • Groups, Geometry, and Dynamics
  • In the theory of random groups, we consider presentations with any fixed num- ber m of generators and many random relators of length l, sending l → ∞. If d is a "density" parameter measuring the rate of exponential growth of the number of relators compared to the length of relators, then many group-theoretic properties become generi- cally true or generically false at different values of d. The signature theorem for this density model is a phase transition from triviality to hyperbolicit y: for… CONTINUE READING

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