TY - JOUR

T1 - Probability densities of random walks in random systems

AU - Havlin, Shlomo

AU - Bunde, Armin

PY - 1989/9

Y1 - 1989/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0008994972&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(89)90189-9

DO - 10.1016/0167-2789(89)90189-9

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AN - SCOPUS:0008994972

SN - 0167-2789

VL - 38

SP - 184

EP - 191

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-3

ER -