Random triangular Burnside groups

We introduce a model for random groups in varieties of $n$-periodic as quotients triangular groups. show that an explicit $d_{\mathrm{crit}}\in(1/3,1/2)$, densities $d\in(1/3,d_{\mathrm{crit}})$ and $n$ large enough, the produces \emph{infinite} As application, we obtain, every fixed enough $n$, $p\in (1,\infty)$ infinite group with points all isometric actions on $L^p$-spaces. Our main contribution is to certain are uniformly acylindrically hyperbolic.