2 problems

Let … is $\varphi$-irreducible over $\mathbf{S}\setminus\mathbf{S}_\eta$ for every $\eta>0$. Negative-invasion extinction conjecture. If $\lambda^*(\mu)<0$ for every invariant meas…

Let … is persistent in probability. The cited theorem proves almost-sure persistence when every invariant boundary measure has a species with positive invasion rate, equivalently u…