We identify the genetic signature of a selective sweep in a population described by a birth-and-death process with density dependent competition. We study the limit behavior for large K, where K scales the population size. We focus on two loci: one under selection and one neutral. We distinguish...

We study a variation of the SIR (Susceptible/Infected/Recovered) dynamics on the complete graph, in which infected individuals may only spread to neighboring susceptible individuals at fixed rate λ0 while recovered individuals may only spread to neighboring infected individuals at fixed rate 1....

We introduce a reversible Markovian coagulation–fragmentation process on the set of partitions of {1,…,L} into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be seen as the Gibbs measure for a homogeneous pinning model...

Constrained diffusions, with diffusion matrix scaled by small ϵ0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under...

We study a model of species survival recently proposed by Michael and Volkov. We interpret it as a variant of empirical processes, in which the sample size is random and when decreasing, samples of smallest numerical values are removed. Micheal and Volkov proved that the empirical distributions...