{"paper":{"title":"Reinforced random walks with geometric inter-transition times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fernando P. A. Prado, Mirela G. Coelho","submitted_at":"2026-06-03T19:43:02Z","abstract_excerpt":"We consider interacting vertex-reinforced random walks on a finite graph, where each walk transitions at independent geometric random times with parameter $p_i \\in (0,1]$. The transition matrix of walk $i$ takes the form $Q^i(x, p_i) = p_i \\Pi^i(x) + (1-p_i)I$, where $\\pi^i(x)$ is the unique invariant measure, independently of $p_i$. Consequently, the limiting points of the occupation measure $X(n)$ coincide with those of the simultaneous-transition model ($p_i = 1$): the solutions of $x = \\pi(x)$. Verifying almost sure convergence to these points is non-trivial, since the stochastic input $U("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05386","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/2606.05386/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"}