{"id":"palomar/PALOMAR-2026-10-19-000003","url":"https://github.com/mmislan/palomar-compartment-division-threshold/tree/c5dacf41f334ccc781c4bda691c388b6214befb2","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-19-000003-v1.json","repo":"https://github.com/mmislan/palomar-compartment-division-threshold","tags":["math.PR","q-bio.MN","msc:60J27","msc:60J80","msc:92C42","stochastic-processes","molecular-biology","branching"],"score":0,"title":"Survival and transience above the compartment-division threshold","trust":"high","domain":"math.PR","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.PR","summary":"Survival and transience are established throughout the strictly supercritical regime of the noncoagulating compartment model of Anderson, Howells and Rojas La Luz (https://arxiv.org/abs/2511.10223v4, Remark 4.8). Compartments produce molecules at rate b, degrade them at rate d per molecule, exit at rate e, and divide at rate f per molecule, with arbitrary conservative allocation between the daughters. For b,e,f > 0 and d >= 0 with bf > e(e+d), every finite nonempty family has positive probability of eternal survival, with an explicit product lower bound. For positive immigration intensity…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-19","reactions":{},"formalized":true,"formalizes":[{"title":"Survival and transience above the compartment-division threshold","identifier":"","relationship":"formalizes"}]}