TY - JOUR
T1 - Random groups arising as graph products
AU - Charney, Ruth
AU - Farber, Michael
PY - 2012
Y1 - 2012
N2 - In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of right-angled Artin and Coxeter groups. We adopt the Erdös and Rényi model of a random graph and find precise threshold functions for hyperbolicity (or relative hyperbolicity). We also study automorphism groups of right-angled Artin groups associated to random graphs. We show that with probability tending to one as n → ∞, random right-angled Artin groups have finite outer automorphism groups, assuming that the probability parameter p is constant and satisfies 0:2929 < p < 1.
AB - In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of right-angled Artin and Coxeter groups. We adopt the Erdös and Rényi model of a random graph and find precise threshold functions for hyperbolicity (or relative hyperbolicity). We also study automorphism groups of right-angled Artin groups associated to random graphs. We show that with probability tending to one as n → ∞, random right-angled Artin groups have finite outer automorphism groups, assuming that the probability parameter p is constant and satisfies 0:2929 < p < 1.
UR - http://www.scopus.com/inward/record.url?scp=84863730554&partnerID=8YFLogxK
U2 - 10.2140/agt.2012.12.979
DO - 10.2140/agt.2012.12.979
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AN - SCOPUS:84863730554
SN - 1472-2747
VL - 12
SP - 979
EP - 995
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 2
ER -