{"paper":{"title":"Many-body contacts in fractal polymer chains and fBm trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"physics.chem-ph","authors_text":"K.E. Polovnikov, M.V. Tamm, S. Nechaev","submitted_at":"2019-01-24T14:16:21Z","abstract_excerpt":"We calculate the probabilities that a trajectory of a fractional Brownian motion with arbitrary fractal dimension $d_f$ visits the same spot $n \\ge 3$ times, at given moments $t_1, ..., t_n$, and obtain a determinant expression for these probabilities in terms of a displacement-displacement covariance matrix. Except for the standard Brownian trajectories with $d_f = 2$, the resulting many-body contact probabilities cannot be factorized into a product of single loop contributions. Within a Gaussian network model of a self-interacting polymer chain, which we suggested recently, the probabilities"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08418","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"}