Quasi-stationary distribution conjecture for N-BBM and N-BRW

Consider $N$-BBM and $N$-BRW, with empirical measures viewed under their invariant measure $\lambda^N$. Quasi-stationary distribution conjecture. Both $N$-BBM and $N$-BRW are ergodic, with a unique invariant measure $\lambda^N$, and the empirical measure distributed according to $\lambda^N$ converges to the delta measure supported on the minimal quasi-stationary distribution. This is the strong selection principle proposed in the source; the source gives no proof or resolution of the assertion.