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Real landscapes exhibit long-range height-height correlations, which are quantified by the Hurst exponent . We give evidence that for negative , in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm-Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for and and a conjecture is proposed for the values in between. By contrast, for positive , we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed. [ABSTRACT FROM AUTHOR]

We propose a probabilistic growth model for transport networks which employs a balance between popularity of nodes and the physical distance between nodes. By comparing the degree of each node in the model network and the World Airline Network (WAN), we observe that the difference between the two is minimized for . Interestingly, this is the value obtained for the node-node correlation function in the WAN. This suggests that our model explains quite well the growth of airline networks. [ABSTRACT FROM AUTHOR]