{"paper":{"title":"Scaling limit for the ant in high-dimensional labyrinths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Fribergh, G\\'erard Ben Arous, Manuel Cabezas","submitted_at":"2016-09-13T18:54:26Z","abstract_excerpt":"We study here a detailed conjecture regarding one of the most important cases of anomalous diffusion, i.e the behavior of the \"ant in the labyrinth\". It is natural to conjecture (see [16] and [8]) that the scaling limit for random walks on large critical random graphs exists in high dimensions, and is universal. This scaling limit is simply the natural Brownian Motion on the Integrated Super-Brownian Excursion. We give here a set of four natural sufficient conditions on the critical graphs and prove that this set of assumptions ensures the validity of this conjecture. The remaining future task"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03977","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"}