{"paper":{"title":"The near-critical Gibbs measure of the branching random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michel Pain","submitted_at":"2017-03-28T20:37:49Z","abstract_excerpt":"Consider the supercritical branching random walk on the real line in the boundary case and the associated Gibbs measure $\\nu_{n,\\beta}$ on the $n^\\text{th}$ generation, which is also the polymer measure on a disordered tree with inverse temperature $\\beta$. The convergence of the partition function $W_{n,\\beta}$, after rescaling, towards a nontrivial limit has been proved by A\\\"{\\i}d\\'ekon and Shi in the critical case $\\beta = 1$ and by Madaule when $\\beta >1$. We study here the near-critical case, where $\\beta_n \\to 1$, and prove the convergence of $W_{n,\\beta_n}$, after rescaling, towards a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09792","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"}