Open Research Index

Survival and transience above the compartment-division threshold

Michael Mislan

Palomar Registrypalomar/PALOMAR-2026-10-19-000003Oct 19, 2026math.PRscore 0

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…

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