TY - JOUR
T1 - Some properties of a random walk on a comb structure
AU - Weiss, George H.
AU - Havlin, Shlomo
PY - 1986/1
Y1 - 1986/1
N2 - We analyze transport properties of a random walk on a comb structure, which serves as a model for a random walk on the backbone of a percolation cluster. It is shown that the random walk along the x axis, which is the analog of the backbone, exhibits anomalous diffusion in that 〈x2(n)〉 ∼ n 1 2, and the expected number of x sites visited is proportional to n 1 4 for large n. The distribution function is found to be a two-dimensional Gaussian. If a field in the x direction, so that diffusion is asymmetric, the expected displacement is found to be asymptotically proportional to n 1 2.
AB - We analyze transport properties of a random walk on a comb structure, which serves as a model for a random walk on the backbone of a percolation cluster. It is shown that the random walk along the x axis, which is the analog of the backbone, exhibits anomalous diffusion in that 〈x2(n)〉 ∼ n 1 2, and the expected number of x sites visited is proportional to n 1 4 for large n. The distribution function is found to be a two-dimensional Gaussian. If a field in the x direction, so that diffusion is asymmetric, the expected displacement is found to be asymptotically proportional to n 1 2.
UR - http://www.scopus.com/inward/record.url?scp=37749053842&partnerID=8YFLogxK
U2 - 10.1016/0378-4371(86)90060-9
DO - 10.1016/0378-4371(86)90060-9
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AN - SCOPUS:37749053842
SN - 0378-4371
VL - 134
SP - 474
EP - 482
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 2
ER -