{"paper":{"title":"Tampered Memory Elephant Random Walk on One-Dimensional Integer Lattice","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Debleena Thacker, Neeraja Sahasrabudhe, Vinita Mulay","submitted_at":"2026-07-30T17:58:36Z","abstract_excerpt":"One of the outstanding questions in the theory of elephant random walks as observed by Gut and Stadtm\\\"uller (2023), is to determine how much memory is needed for a phase transition between the diffusive, critical and superdiffusive regimes to persist. To investigate this memory breakpoint, we introduce the tampered memory elephant random walk, in which the memory is partitioned into two disjoint sets $D_n$ and $D_n^c$, which may be deterministic or random. On $D_n^c$ the dynamics is the same as an elephant random walk, while on $D_n$ the increments are replaced by independent innovations. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28614","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28614/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}