Asymptotic Shapes for Ergodic Families of Metrics on Nilpotent Groups

@inproceedings{Cantrell2015AsymptoticSF,
  title={Asymptotic Shapes for Ergodic Families of Metrics on Nilpotent Groups},
  author={Michael A Cantrell and A. I. Furman},
  year={2015}
}
Let Gamma be a finitely generated nilpotent group. We consider three closely related problems: (i) the asymptotic cone for an equivariant ergodic family of inner metrics on Gamma, generalizing Pansu's theorem; (ii) the limit shapes for First Passage Percolation for general (not necessarily independent) ergodic processes on edges of a Cayley graph of Gamma; (iii) a sub-additive ergodic theorem over a general ergodic Gamma-action. The limiting objects are given in terms of a Carnot-Caratheodory… CONTINUE READING

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SHOWING 1-10 OF 10 REFERENCES

) , no . 3 , 689 – 714 ( French , with English summary ) Geometry of locally compact groups of polynomial growth and shape of large balls

Gromov
  • Adv . Soviet Math . , vol . 9 , Amer . Math . Soc .
  • 1992

Burago

D. Yu
  • Periodic metrics, Representation theory and dynamical systems, Adv. Soviet Math., vol. 9, Amer. Math. Soc., Providence, RI
  • 1992
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