Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Brownian motion and transport II

DY 22.8: Talk

Thursday, March 26, 2009, 12:15–12:30, ZEU 118

On moments and scalings in random walks — Michael Schmiedeberg, •Vasily Zaburdaev, and Holger Stark — Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany

Anomalous diffusion is commonly characterized by an exponent in the power law behavior of the mean square displacement as a function of time. In many cases this exponent does not provide any information about the scaling properties of the probability density function, not mentioning some superdiffusive regimes with a divergent second moment. However, the study of fractional moments can reveal the missing information. For the class of coupled random walks, one of them is the famous Levy walk model, we systematically analyze three methods used to analytically obtain characteristic exponents for the mean square displacement, scaling of the central part and the asymptotic profile of the probability density function. For example, we show that the scaling of the central part of the probability density can be determined using fractional moments <|r|^q> with q≪ 1. These methods deliver distinct and complementary information about an underlying stochastic process. We show how our results can be accessed from experimental data.