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August 14, 2026Journal of Physics A Mathematical and TheoreticalOpen Access

Size-structured populations with growth fluctuations: Feynman-Kac formula and decoupling

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Authors

ELEthan LevienYHYaïr HeinFJFarshid Jafarpour

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Overview

Theoretical modeling demonstrates decoupling between internal states and cell size in fluctuating populations, highlighting simplified population calculations via the Feynman-Kac formula.

Key Points

  • Investigate the mathematical conditions governing asymptotic decoupling between fluctuating internal cellular variables and cell size in heterogeneous, growing populations.
  • Formulated a size-structured population model coupling individual growth rates to fluctuating internal phenotypic variables such as gene expression.
  • Applied the Feynman-Kac formula, random time changes, and exponential tilting to bridge single-lineage dynamics with population-level phenotype distributions under growth-rate selection.
  • Derived exact mathematical conditions required for the internal phenotypic variable to decouple asymptotically from cell size across lineage and population ensembles.
  • Demonstrated that dual-ensemble decoupling allows size dynamics to map to a growth-homogeneous process via random time change, enabling population expectations to be solved via exponential tilting.
  • Characterized weaker, ensemble-specific decoupling regimes and generalized tilted expectations to mass-weighted phenotype distributions.

Cite This Study

Levien et al. (2026) studied this question.

synapsesocial.com/papers/6a7ec69fb70b84ec8b912bb6https://doi.org/10.1088/1751-8121/ae98c4
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