13 problems

Let $N=\sum_{m=2}^{n}I_{[\tau_m>0]}$ be the number of states visited by the process. Visited-state conjecture. In an earlier version of the manuscript, the authors conjectured that…

Let $p\in[0,1]$, and let $X_p(t)$ denote the limiting process describing the number of frozen vertices in the critical window at time $t$. Contat–Curien's conjecture. For every…

Let $\mathcal I$ be a randomly sampled individual, and for $k\in\mathbb N_0$ let $\mathscr E_k$ be the event that there is a coalescence event between $\mathcal A_k$ and…

Conjecture. Theorem 1 remains valid under the additional assumption that $\rho_k<\infty$ for all $k\in E$.

Let $\bm R(t)=\bm r(\tau(t))$ be the process obtained from the replicator coalescent, and let $\bm x^*$ be an evolutionarily stable strategy for the matrix $\bm A$, so that the cor…

Let an SMC algorithm use a stochastic rounding resampling scheme satisfying the standing assumption, and suppose that the incremental transition densities $g_t(x,x')$ satisfy … for…

Single entrance-law conjecture. There is a single entrance law for the nested Kingman coalescent.

The noisy pseudo-marginal algorithm is considered for inference in an 11-dimensional posterior arising from a $\Lambda$-coalescent model. The algorithm's trace plot exhibits residu…

Let $\beta$-coalescents be coalescent processes characterized by the beta measure with parameters $(1+\alpha,1-\alpha)$, and let $\Pi_\text{L�vy}$ denote the coalescent process ass…

Aldous's continuum random tree pruning yields an interval-partition-valued process, and the paintbox procedure associates such a process with a partition-valued coalescent. The pro…

Let $\Lambda$ be the measure governing a $\Lambda$ Fleming–Viot process, and consider the regime of intensive infinity, the regime denoted by $\textsc{Intensive}\ \infty$ in the so…

Let $\Lambda$ be the measure governing a $\Lambda$ Fleming–Viot process, and consider the regime of intensive dust, meaning the regime in which the dust component is present. An Ev…

Smoothness conjecture. The function $\rho_{\mathsf{BF}}$ should be smooth on $[t_{\mathsf c},\infty)$. If so, its right derivative at the critical time satisfies