title: Optimal estimates of the diffusion coefficient of a single Brownian trajectory.
abstract: Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry, and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single-particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way to extract diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least-squares estimate. Furthermore, we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.
authors.affiliation: Instituto de Física, Universidad Nacional Autonoma de México, DF, México. boyer@fisica.unam.mx
authors.forename: Denis
authors.initials: D
authors.lastname: Boyer
authors.forename: David S
authors.initials: DS
authors.lastname: Dean
authors.forename: Carlos
authors.initials: C
authors.lastname: Mejía-Monasterio
authors.forename: Gleb
authors.initials: G
authors.lastname: Oshanin
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical