{"paper":{"title":"Schramm-Loewner Evolution and isoheight lines of correlated landscapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"H. J. Herrmann, K. J. Schrenk, N. A. M. Araujo, N. Pose","submitted_at":"2015-08-31T18:18:25Z","abstract_excerpt":"Real landscapes are usually characterized by long-range height-height correlations, which are quantified by the Hurst exponent $H$. We analyze the statistical properties of the isoheight lines for correlated landscapes of $H\\in [-1,1]$. We show numerically that, for $H\\leq 0$ the statistics of these lines is compatible with $SLE$ and that established analytic results are recovered for $H=-1$ and $H=0$. This result suggests that for negative $H$, in spite of the long-range nature of correlations, the statistics of isolines is fully encoded in a Brownian motion with a single parameter in the con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07942","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}