4 papers · 1 filter
Branch lengths for geodesics in the directed landscape and mutation patterns in growing spatially structured populations
Shirshendu Ganguly, Jason Schweinsberg, Yubo Shuai
Consider a population that is expanding in two-dimensional space. Suppose we collect data from a sample of individuals taken at random either from the entire population, or from ne…
The Accumulation of Beneficial Mutations and Convergence to a Poisson Process
Nantawat Udomchatpitak, Jason Schweinsberg
We consider a model of a population with fixed size , which is subjected to an unlimited supply of beneficial mutations at a constant rate . Individuals with beneficia…
The Yaglom limit for branching Brownian motion with absorption and slightly subcritical drift
Julien Berestycki, Jiaqi Liu, Bastien Mallein +1
Consider branching Brownian motion with absorption in which particles move independently as one-dimensional Brownian motions with drift , each particle splits into two particl…
Phase transition of the consistent maximal displacement of branching Brownian motion
Julien Berestycki, Jiaqi Liu, Bastien Mallein +1
Consider branching Brownian motion in which we begin with one particle at the origin, particles independently move according to Brownian motion, and particles split into two at rat…