Uniform Explosion-Time Tails and Sharp Scaling Laws in a Two-Species Stochastic Reaction Network

For a specific two-species autocatalytic open-feed stochastic mass-action network, we prove almost-sure finite-time explosion from every state with an initially positive A population, a uniform O(1/sqrt(A)) expected-explosion-time bound, a uniform exponential tail for the scaled explosion time, and sharp large-population scaling limits with all positive moment convergence. The deterministic limiting explosion time is given by an explicit integral for arbitrary initial B/sqrt(A) ratio, including zero. The result concerns a restricted non-weakly-reversible idealized network and does not describe a finite-fuel physical reactor or solve a general stochastic reaction network conjecture. Historical novelty and independent peer review are unverified. Full verification scripts and recorded stochastic finite-threshold simulations are included.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-05
DOI
https://doi.org/10.5281/zenodo.23955832
Primary Topic
Stochastic processes and statistical mechanics
Type
preprint
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preprint

Uniform Explosion-Time Tails and Sharp Scaling Laws in a Two-Species Stochastic Reaction Network

Kias Henry
Zenodo (CERN European Organization for Nuclear Research)
Stochastic processes and statistical mechanics
preprint

Uniform Explosion-Time Tails and Sharp Scaling Laws in a Two-Species Stochastic Reaction Network

Kias Henry
preprint en

Abstract

For a specific two-species autocatalytic open-feed stochastic mass-action network, we prove almost-sure finite-time explosion from every state with an initially positive A population, a uniform O(1/sqrt(A)) expected-explosion-time bound, a uniform exponential tail for the scaled explosion time, and sharp large-population scaling limits with all positive moment convergence. The deterministic limiting explosion time is given by an explicit integral for arbitrary initial B/sqrt(A) ratio, including zero. The result concerns a restricted non-weakly-reversible idealized network and does not describe a finite-fuel physical reactor or solve a general stochastic reaction network conjecture. Historical novelty and independent peer review are unverified. Full verification scripts and recorded stochastic finite-threshold simulations are included.

Zenodo (CERN European Organization for Nuclear Research)
Stochastic processes and statistical mechanics
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