Circles in the Morse boundaries of random right-angled Coxeter groups

Let $n$-vertex graphs be sampled from a random graph model with density greater than $1/n$ and bounded away from $1$, and let the associated right-angled Coxeter group be the group defined by the graph. Random Morse-boundary circle conjecture. For any density greater than $1/n$ and bounded away from $1$, asymptotically almost surely the random right-angled Coxeter group contains circles in its Morse boundary. In particular, it is not virtually a right-angled Artin group. The conjecture is motivated by known results that, for a large range of density functions, random graphs asymptotically almost surely produce right-angled Coxeter groups with quadratic divergence, and that such graphs contain large induced polygons. Establishing the claimed circles in the Morse boundary would distinguish these groups from right-angled Artin groups and rule out virtual right-angled Artin structure.