7 problems

Jump-representation conjecture. The jump representation of the tree-valued Markov process holds without the Grey condition.

Let $\Lambda\in\mathcal M_f([0,1])$, and let $\mathcal V^\Lambda_t$ be the tree-valued $\Lambda$-resampling dynamics at time $t$. Write $\mathbb U_c$ for the space of compact metri…

Let $\mathcal V^\Lambda=(\mathcal V_t^\Lambda)_{t\geq 0}$ be the tree-valued $\Lambda$-resampling dynamics. Atomlessness conjecture. For Lebesgue almost every $t$, the metric measu…

Let $\mathcal V^\Lambda$ be the tree-valued $\Lambda$-resampling dynamics associated with a finite measure $\Lambda\in\mathcal M_f([0,1])$. Continuous-paths conjecture. The followi…

Let $\Lambda\in\mathcal M_f([0,1])$ satisfy the dust-free condition … For the corresponding tree-valued $\Lambda$-Cannings dynamics $\mathcal V^{N,\Lambda}$, suppose there is a ran…

Light-tail Cannings conjecture. Under a suitable time rescaling, $(\mathcal V^N)_{N\in\mathbb N}$ converges weakly to the tree-valued Fleming–Viot dynamics in the Skorohod topology…

Let $cmathcal U^N$ denote an exchangeable tree-valued population dynamics with population size $N$, and let $cmathcal U=(cmathcal U_t)_{t\beq 0}$ be the tree-valued Fleming–Viot dy…