Continuous time random walks and their close relatives

Date

Oct 16, 2015

Time

2:00 PM - 3:00 PM

Speaker

Igor M. Sokolov

Affiliation

Humboldt-Universität zu Berlin

Language

en

Main Topic

Physik

Other Topics

Physik

Host

Advanced Study Group Klages

Description

Continuous time random walks (CTRW) are a popular model of anomalous diffusion. The model has a clear physical interpretation as an approximate description of trapping in high dimensions, and a clear mathematical structure as a process subordinated to simple random walks, and, in the corresponding limit, to Brownian motion. We discuss several models closely related to CTRW. Thus, we show that the scaled Brownian motion (sBm) as described by the Bachelor's equation (in the subdiffusive case) is a mean field (Gaussian) approximation of CTRW, and discuss the similarities and the differences between these models. Both models are non-stationary and share the same aging properties, but differ in the finer characteristics of their behavior. Thus the sBm is weakly ergodic [1] while CTRW shows weak ergodicity breaking. We moreover consider other situations corresponding to more general models of motion in random potentials [2] and to models subordinated to fractional Brownian motion [3]. In cases when the behavior can be described by subordination, we discuss which properties are dominated by the parent process and which ones (like the ergodicity breaking parameter) by the directing one.

Last modified: Oct 16, 2015, 10:04:06 AM