{"id":"2ea9e103-733b-4a58-8b47-9a6eba8c62ce","arxiv_id":"2411.08018","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"For i.i.d. weights with P(X>t)~Ct^{-2}, the last passage time is shown to be at least c n(log n)^{3/4}/log log n with high probability, and a finite-second-moment distribution is exhibited whose last passage time grows superlinearly.","lead":"This paper proves the first rigorous lower bounds for last passage percolation in two critical random environments: heavy-tailed weights with an inverse-square tail, and the branching random walk. It also answers a 2002 question of Martin by showing that finite second moment of the weights does not guarantee linear growth of the passage time.","discovery_kind":"new_method","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-12T22:03:29.547984+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}