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Metastability and multiscale extinction time on a finite system of interacting stochastic chains

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  • Brochini, L.
  • Abadi, M.

Abstract

We investigate the metastability and extinction time of a finite discrete-time system composed of a large number of interacting components, using both analytical and numerical methods. The system is Markovian with respect to the potential profiles of the components, which are simultaneously subject to leakage and gain effects. We show that the only invariant measure is the null configuration, implying that the system almost surely ceases activity in finite time. Additionally, the system exhibits a metastable state and a metastable barrier, which governs the characteristic timescale of the system’s lifetime. We identify a critical parameter, determined by the balance between leakage and gain, below which the extinction time is independent of system size. Above this critical value, the extinction time depends on the number of components, exhibiting infinitely many scaling behaviors governed by a nontrivial relationship among leakage, gain, and system size.

Suggested Citation

  • Brochini, L. & Abadi, M., 2026. "Metastability and multiscale extinction time on a finite system of interacting stochastic chains," Stochastic Processes and their Applications, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:spapps:v:196:y:2026:i:c:s0304414926000360
    DOI: 10.1016/j.spa.2026.104904
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