2 citations · 7 across the 6 of their papers we have counts for
7 papers
Random groups do not have Property (T) at densities below 1/4
Calum J Ashcroft
We prove that random groups in the Gromov density model at density d <1/4 do not have Property (T), answering a conjecture of Przytycki. We also prove similar results in the k-angu…
Property (T) in random quotients of hyperbolic groups at densities above 1/3
Calum J. Ashcroft
We study random quotients of a fixed non-elementary hyperbolic group in the Gromov density model. Let be a finite presentation of a non-elementary…
Link Conditions for the Haagerup Property
Calum J. Ashcroft
We provide a condition on the links of a polygonal complex X that is sufficient to ensure Aut(X) has the Haagerup property, and hence so do any closed subgroups of Aut(X) (in parti…
Property (T) in density-type models of random groups
Calum J. Ashcroft
We study Property (T) in the model of random groups: as tends to infinity this gives the Gromov density model, introduced in [Gro93]. We provide bounds for Property…
On the eigenvalues of Erdos-Renyi random bipartite graphs
Calum J. Ashcroft
We analyse the eigenvalues of Erdös--Rényi random bipartite graphs. In particular, we consider satisfying $n_{2}p=Ω(\sqrt{n_{2}p}\log^…
Link conditions for cubulation
Calum J. Ashcroft
We provide a condition on the links of polygonal complexes that is sufficient to ensure groups acting properly discontinuously and cocompactly on such complexes contain a virtually…
On random presentations with fixed relator length
C. J. Ashcroft, Colva M. Roney-Dougal
The standard model of random groups is a model where the relators are chosen randomly from the set of cyclically reduced words of length on an -element generatin…