We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seed-bank effect. More precisely, we consider a simple seed-bank age distribution with two atoms, leading to either classical or long ge
nealogical jumps (the latter modeling the effect of seed-dormancy). We assume that the length of these long jumps scales like a power $N^beta$ of the original population size $N$, thus giving rise to a `strong seed-bank effect. For a certain range of $beta$, we prove that the ancestral process of a sample of $n$ individuals converges under a non-classical time-scaling to Kingmans $n-$coalescent. Further, for a wider range of parameters, we analyze the time to the most recent common ancestor of two individuals analytically and by simulation.
We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Greens function of the discrete Bilaplacian. This is interpreted as a model for a semiflexible membrane. $d=4$ is the
critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.
