6 problems

Consider the long-range percolation graph on $\mathbb T_n^d$ with all nearest-neighbour edges and each non-nearest-neighbour edge included independently with probability…

Consider the competing long-range infection model on $\mathbb T_n^d$ with long-range parameters $\alpha_\ominus(n)$ and $\alpha_\oplus(n)$, infection-rate ratio $\lambda(n)$, and c…

Consider the competing long-range infection model and the notation of the theorem concerning absence of coexistence, including the final-size quantity $M_n$ and the parameter $Z_n$…

Consider the system of interacting Wright–Fisher diffusions on $\mathbb Z^d$ with $N=1$ and parameter $\mu>1$, where $s$ is the selection parameter and coexistence refers to long-t…

Let the symmetric Neuhauser–Pacala model be the competing-species system on the lattice $\mathbb Z^d$, with coexistence meaning that both species persist in the long term. Neuhause…

Let $d\geq 3$ and let $\varrho>0$. In the two-type symbiotic branching model $\textrm{SBM}_\gamma(\varrho)$ on $\mathbb{Z}^d$, coexistence means that there are summable initial con…