An invariance property of diffusive random walks
Abstract
Starting from a simple animalbiology example, a general, somewhat counterintuitive property of diffusion random walks is presented. It is shown that for any (nonhomogeneous) purely diffusing system, under any isotropic uniform incidence, the average length of trajectories through the system (the average length of the random walk trajectories from entry point to first exit point) is independent of the characteristics of the diffusion process and therefore depends only on the geometry of the system. This exact invariance property may be seen as a generalization to diffusion of the wellknown meanchordlength property (Case K. M. and Zweifel P. F., Linear Transport Theory (AddisonWesley) 1967), leading to broad physics and biology applications.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 January 2003
 DOI:
 10.1209/epl/i200300208x
 Bibcode:
 2003EL.....61..168B
 Keywords:

 05.60.Cd;
 05.40.a;
 Classical transport;
 Fluctuation phenomena random processes noise and Brownian motion