Probability densities of random walks in random systems

Shlomo Havlin, Armin Bunde

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


We review recent results for the probability distribution of random walkers in random systems, where diffusion is anomalous and the mean-square displacement scales with time as R2(t)∼t2 w, dw > 2. The random systems are characterized by structural disorder and by random transition rates. In general, the mean distribution function 〈P(r, t)〉 of the random walkers is a stretched Gaussian and scales as log[ P(r,t) P(r,0)]∼-[ r R(t)]u, where u= dw (dw-1). On random fractals, the fluctuations of the density distribution P(r, t), for fixed distance r and time t, have a broad logarithmic distribution. The average moments 〈Pq〉 scale in a multifractal way as 〈P〉τ(q), where τ(q)∼qτ,γ<1. In contrast, in chemical l-space the fluctuations of P are narrow and 〈Pq〉∼〈P〉q.

Original languageEnglish
Pages (from-to)184-191
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Issue number1-3
StatePublished - Sep 1989


Dive into the research topics of 'Probability densities of random walks in random systems'. Together they form a unique fingerprint.

Cite this