The square model for random groups

Tomasz Odrzygóźdź. "The square model for random groups." Colloquium Mathematicae 142.2 (2016): 227-254. <http://eudml.org/doc/286455>.

@article{TomaszOdrzygóźdź2016,
abstract = {We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model does not have Property (T). Inspired by the results for the triangular model, we prove that for densities < 1/4 in the square model, a random group is free with overwhelming probability. We also introduce abstract diagrams with fixed edges and prove a generalization of the isoperimetric inequality.},
author = {Tomasz Odrzygóźdź},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {227-254},
title = {The square model for random groups},
url = {http://eudml.org/doc/286455},
volume = {142},
year = {2016},
}

TY - JOUR
AU - Tomasz Odrzygóźdź
TI - The square model for random groups
JO - Colloquium Mathematicae
PY - 2016
VL - 142
IS - 2
SP - 227
EP - 254
AB - We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model does not have Property (T). Inspired by the results for the triangular model, we prove that for densities < 1/4 in the square model, a random group is free with overwhelming probability. We also introduce abstract diagrams with fixed edges and prove a generalization of the isoperimetric inequality.
LA - eng
UR - http://eudml.org/doc/286455
ER -