{"paper":{"title":"The continuum disordered pinning model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francesco Caravenna, Nikos Zygouras, Rongfeng Sun","submitted_at":"2014-06-19T15:50:08Z","abstract_excerpt":"Any renewal processes on $\\mathbb{N}$ with a polynomial tail, with exponent $\\alpha \\in (0,1)$, has a non-trivial scaling limit, known as the $\\alpha$-stable regenerative set. In this paper we consider Gibbs transformations of such renewal processes in an i.i.d. random environment, called disordered pinning models. We show that for $\\alpha \\in (1/2, 1)$ these models have a universal scaling limit, which we call the continuum disordered pinning model (CDPM). This is a random closed subset of $\\mathbb{R}$ in a white noise random environment, with subtle features:\n  -Any fixed a.s. property of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5088","kind":"arxiv","version":2},"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"}