Cogrowth and spectral gap of generic groups

Yann Ollivier[1]

  • [1] UMPA - CNRS, École normale supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07 (France)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 1, page 289-317
  • ISSN: 0373-0956

Abstract

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The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.

How to cite

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Ollivier, Yann. "Cogrowth and spectral gap of generic groups." Annales de l’institut Fourier 55.1 (2005): 289-317. <http://eudml.org/doc/116189>.

@article{Ollivier2005,
abstract = {The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.},
affiliation = {UMPA - CNRS, École normale supérieure de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07 (France)},
author = {Ollivier, Yann},
journal = {Annales de l’institut Fourier},
keywords = {Random groups; cogrowth; hyperbolic groups; random walk on groups; random groups; random walks on groups; cogrowth exponents; free groups},
language = {eng},
number = {1},
pages = {289-317},
publisher = {Association des Annales de l'Institut Fourier},
title = {Cogrowth and spectral gap of generic groups},
url = {http://eudml.org/doc/116189},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Ollivier, Yann
TI - Cogrowth and spectral gap of generic groups
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 1
SP - 289
EP - 317
AB - The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.
LA - eng
KW - Random groups; cogrowth; hyperbolic groups; random walk on groups; random groups; random walks on groups; cogrowth exponents; free groups
UR - http://eudml.org/doc/116189
ER -

References

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  14. Y. Ollivier, Sharp phase transition theorems for hyperbolicity of random groups, Geom. Funct. Anal. 14 (2004), 595-679 Zbl1064.20045MR2100673
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