8 problems

Logarithmic extinction-rate conjecture.

Quasi-stationary extinction-event conjecture.

Quasi-stationary distribution conjecture. Then:

Let $n$ be the population-size scaling parameter, let $I_h^n(t)$ and $I_v^n(t)$ denote infected hosts and infected vectors, and let $\mathcal{R}_0$ be the basic reproduction number…

Let $n$ be the host population size, let $I_h^n(t)$ denote the number of infected hosts at time $t$, and let $\mathcal{R}_0$ be the basic reproduction number. When…

Let $p$ and $q$ be the right- and left-jump rates, respectively, with $q>p$, and let $\rho^N$ be the equilibrium density of the Fleming–Viot process driven by the nearest-neighbor…

Let $Z=(Z_t,t\geq0)$ be a Markov driving process on $\Lambda\cup\{0\}$, with $0$ absorbing, and let $\tau$ be its absorption time. For $N\geq2$, let…

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 ergod…