8 problems

Consider the spatial contact process with mutations on a graph, with birth rate $lambda$ and mutation probability $r$, where pathogens of the same type die simultaneously and each…

Let $s$ and $\lambda$ be the parameters of the generalized Poisson offspring distribution, let $P_{\rm{GP}}^\infty$ be its extinction probability, and let $P_{\rm{GP}}^{(n)}$ and…

Survival-probability convergence conjecture. The conclusion of Theorem concerning the asymptotic survival probability remains valid for cones that are not pyramids, provided the pa…

Let $T$ be the survival time of the Brownian particle among moving traps, and let $d\geq 3$. Define the Lyapunov exponent by … The source states that this limit exists and is posit…

Let $\lambda_l(\mathbb{T})$ and $\lambda_c(\mathbb{T})$ denote the local and global survival thresholds for the Williams–Bjerknes model on the regular tree $\mathbb{T}^d$. For…

Continuous–discrete survival-probability conjecture. For any process $X$ from the class $\mathcal{X}$, under suitable conditions on $\mathcal{I}$, these probabilities should be com…

Critical extinction conjecture. When $\Psi=0$,

Consider a binary tree ${\mathbb T}_{\tt bs}$ rooted at $e$, with independent identically distributed Bernoulli increments $Y(x)$ of mean $p\in(0,1/2)$, and define the branching ra…