Claus Metzner. 1d analysis of 2d isotropic random walks

Natural Sciences / Physics / Biophysics

Submitted on: Aug 19, 2012, 19:34:28

Description: Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of the underlying stochastic process. Often, it can be assumed {em a priori} that the underlying discrete-time random walk model is independent from absolute position (homogeneity), direction (isotropy) and time (stationarity). In this article we first review some common statistical methods for analyzing 2D trajectories, based on quantities with built-in rotational invariance. We then discuss an alternative approach in which the two-dimensional trajectories are reduced to one dimension by projection onto an arbitrary axis and rotational averaging. Each step of the resulting 1D trajectory is further factorized into sign and magnitude.

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