{"paper":{"title":"Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"Makiko Sato, Makoto Katori","submitted_at":"2011-01-20T11:51:54Z","abstract_excerpt":"As an image of the many-to-one map of loop-erasing operation $\\LE$ of random walks, a self-avoiding walk (SAW) is obtained. The loop-erased random walk (LERW) model is the statistical ensemble of SAWs such that the weight of each SAW $\\zeta$ is given by the total weight of all random walks $\\pi$ which are inverse images of $\\zeta$, $\\{\\pi: \\LE(\\pi)=\\zeta \\}$. We regard the Brownian paths as the continuum limits of random walks and consider the statistical ensemble of loop-erased Brownian paths (LEBPs) as the continuum limits of the LERW model. Following the theory of Fomin on nonintersecting L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3874","kind":"arxiv","version":3},"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"}