{"paper":{"title":"Exact and limit distributions of the largest fitness on correlated fitness landscapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"cond-mat.stat-mech","authors_text":"Abhishek Dasgupta, Gayatri Das, Kavita Jain","submitted_at":"2009-09-22T09:01:27Z","abstract_excerpt":"We study the distribution of the maximum of a set of random fitnesses with fixed number of mutations in a model of biological evolution. The fitness variables are not independent and the correlations can be varied via a parameter $\\ell=1,...,L$. We present analytical calculations for the following three solvable cases: (i) one-step mutants with arbitrary $\\ell$ (ii) weakly correlated fitnesses with $\\ell=L/2$ (iii) strongly correlated fitnesses with $\\ell=2$. In all these cases, we find that the limit distribution for the maximum fitness is not of the standard Gumbel form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3933","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"}