Non-residual-finiteness conjecture for random BMW groups

A BMW group is a group acting on a product of two regular trees, and a BMW group of degree $(m,n)$ has tree factors of degrees $m$ and $n$. In the range $n>m^5$, consider the random BMW group from the paper's random model. A group is residually finite if every nontrivial element survives in some finite quotient, and virtually simple if it has a simple subgroup of finite index. Non-residual-finiteness conjecture. In the above range of $m$ and $n$, a random BMW group is asymptotically almost surely not residually finite and consequently is virtually simple by Theorem~. This predicts that the random model typically produces virtually simple groups, beyond the established high-probability hereditary just-infiniteness result; the status of the conjecture is not specified in the source.