Convergence of random walks to Brownian motion in phylogenetic tree-space

摘要: The set of all phylogenetic (or evolutionary) trees for a fixed species forms manifold-stratified geodesic metric space known as Billera-Holmes-Vogtmann tree-space. In order to analyse samples it is desirable construct parametric distributions on this space, but task very challenging. One way such consider particles undergoing Brownian motion in tree-space from starting point. distribution the after given duration time analogous multivariate normal Euclidean space. Since these cannot be worked with directly, we approximating them by suitably defined random walks We prove that number steps tends infinity and step-size zero, determined transition kernel walk converges corresponding motion. This result opens up possibility statistical modelling using obtained kernels methods developed here could extended establish similar results other complexes or spaces.