10 problems

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…

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 predator–prey system … where $s$ is prey biomass, $x_i$ are predator biomasses, and $a_i,m_i,\lambda_i$ are the parameters defined by the nondimensionalisation in the…

Let $d\geq 2$. Consider the two-type Richardson model on $\mathbb{Z}^d$, with $FPP_1$ initialized at the origin and $FPP_{\lambda}$ spreading from a single seed activated at time…

Let $\operatorname{FPP}_1$ and $\operatorname{FPP}_\lambda$ be competing first passage percolation processes, with respective passage-rate parameters $1$ and $\lambda$, started fro…

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…

Consider a branching process with a degree-dependent starting rule that colors sufficiently high-degree individuals red or blue, followed by a flow rule in which each vertex takes…

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…