5 problems

The paper considers Theorems 1 and 2 concerning the existence and characterization of a self-similar measure-valued process and its associated Lamperti transformation. Generalizati…

Multitype coalescent speed conjecture. Provided the conditions of the theorem establishing coming down from infinity hold, the ordinary differential equation

Moment approximation conjecture. The moments of $X_{n,k}$ differ only little from those of $p_{k-1}^{(a)}X_n$ if $n$ is sufficiently large.

Conjecture. Then

For each fixed sample size $k\ge1$, let $(\Pi_t^{k,N},t\ge0)$ be the ancestral partition process of a population of size $N$, restricted to the sample, and let $(\Pi_t^k,t\ge0)$ de…