7 problems

Total-length process conjecture. The sequence of stationary processes

Total-length fluctuation conjecture. As $n\to\infty$,

Let $\hat \ell_n:=\ell_n-\bar \ell_n$ be the total internal branch length of an $n$-coalescent, where $\ell_n$ is its total length and $\bar \ell_n$ is its total external branch le…

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…