{"paper":{"title":"H\\\"older Regularity and Dimension Bounds for Random Curves","license":"","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"math.FA","authors_text":"Almut Burchard, Michael Aizenman","submitted_at":"1998-01-07T15:32:02Z","abstract_excerpt":"Random systems of curves exhibiting fluctuating features on arbitrarily small scales ($\\delta$) are often encountered in critical models. For such systems it is shown that scale-invariant bounds on the probabilities of crossing events imply that typically all the realized curves admit H\\\"older continuous parametrizations with a common exponent and a common random prefactor, which in the scaling limit ($\\delta\\to 0$) remains stochastically bounded. The regularity is used for the construction of scaling limits, formulated in terms of probability measures on the space of closed sets of curves. Un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9801027","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9801027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}