%0 Journal Article %1 WOS:000426590000008 %A Pose, N %A Schrenk, K J %A Araujo, N A M %A Herrmann, H J %C 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE %D 2018 %I WORLD SCIENTIFIC PUBL CO PTE LTD %J INTERNATIONAL JOURNAL OF MODERN PHYSICS C %K Schramm-Loewner accessible evolution} lines; perimeter; {Isoheight %N 1 %R 10.1142/S0129183118500080 %T Schramm-Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes %V 29 %X Real landscapes exhibit long-range height-height correlations, which are quantified by the Hurst exponent H. We give evidence that for negative H, 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 H = -1 and H = 0 and a conjecture is proposed for the values in between. By contrast, for positive H, we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.

@article{WOS:000426590000008, abstract = {Real landscapes exhibit long-range height-height correlations, which are quantified by the Hurst exponent H. We give evidence that for negative H, 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 H = -1 and H = 0 and a conjecture is proposed for the values in between. By contrast, for positive H, we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}, author = {Pose, N and Schrenk, K J and Araujo, N A M and Herrmann, H J}, biburl = {https://www.bibsonomy.org/bibtex/2f5248e96ad33a70abf49ec5c1d755e26/ppgfis_ufc_br}, doi = {10.1142/S0129183118500080}, interhash = {e82d004596a7c2d8827e81e903f45f1f}, intrahash = {f5248e96ad33a70abf49ec5c1d755e26}, issn = {0129-1831}, journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS C}, keywords = {Schramm-Loewner accessible evolution} lines; perimeter; {Isoheight}, number = 1, publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Schramm-Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes}, tppubtype = {article}, volume = 29, year = 2018 }