{"paper":{"title":"Diffusive and Super-Diffusive Limits for Random Walks and Diffusions with Long Memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"B\\'alint T\\'oth","submitted_at":"2018-12-30T09:52:14Z","abstract_excerpt":"We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\\Bbb R}^d$ or ${\\Bbb Z}^d$. The first class consists of random walks on ${\\Bbb Z}^d$ in divergence-free random drift field, modelling the motion of a particle suspended in time-stationary incompressible turbulent flow. The second class consists of self-repelling random diffusions, where the diffusing particle is pushed by the negative gradient of its own occupation time measure towards regions less visited in the past. We establish normal diffusion (with square-root-of-time scaling a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11500","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"}