{"paper":{"title":"Criticality conditions in the Derrida-Retaux model with a random number of terms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexey Lotnikov, Anna Kotova","submitted_at":"2025-02-04T18:00:02Z","abstract_excerpt":"The article considers the Derrida-Retaux model with a random number of terms, i.e. a sequence of integer random variables defined by the relations $ X_{n + 1} = (X_n^{(1)} + X_n^{(2)} + ... + X_n^{(N_n)} - a)^{+}$, $n\\ge 0$, where $X_n^{j}$ are independent copies of $X_n$, the values of $N_j$ are independent and identically distributed, $a$ is a positive integer. The energy in the model is defined as $Q:=\\lim\\limits_{n\\to\\infty} \\frac{\\mathbb{E}(X_{n})}{(\\mathbb{E}N_1)^{n}}$. We present sufficient conditions (in terms of distributions of $X_0$ and $N_1$) for subcritical ($Q=0$) and supercritic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02535","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/2502.02535/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"}