Random triangular groups at density 1/3

Abstract

Let Γ(n,p) denote the binomial model of a random triangular group. We show that there exist constants c, C > 0 such that if p <= c/n^2, then a.a.s. Γ(n,p) is free and if p >= C log n/n^2 then a.a.s. Γ(n,p) has Kazhdan's property (T). Furthermore, we show that there exist constants C',c' > 0 such that if C'/n^2 <= p <= c' log n/n^2, then a.a.s. Γ(n,p) is neither free nor has Kazhdan's property (T).

References in corpus (1)

• Random groups and Property (T): Żuk's theorem revisited

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