5 problems

Let $(S_\ell)$ be the special sequence described at the beginning of the section, and let $\mathfrak F_\ell$ be the random labelled forests associated with the coalescing partition…

Consider the semi-pushed branching Brownian motion regime, in which $\alpha\in(1,2)$ and the population-size processes converge, under the scaling described in the source, to an…

Let $\tilde h^\tinfty$ denote the invariant spatial distribution of particles, and suppose that, for some slowly varying function $\ell$ and $alpha\backslashin(1,2)$, condition … h…

Let $u{n,beta}$ be the Gibbs measure on particles at generation $n$, let $u{n,beta}^{otimes 2}$ denote its product measure on two sampled particles $z,z'$, and let…

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…