Systematic theory of contact eigenvalue problems

Develop a systematic variational and geometric theory of contact eigenvalue problems in the large-deviation setting, including the role of contact eigenvectors, the accuracy of the symplectic reduction, and the construction of driven processes realizing atypical fluctuations in supercritical growing systems.

Background

The moment calculation uses a symplectic reduction of a contact eigenvalue problem because the exact problem is technically difficult. The authors state that the variational and geometric structure of these contact eigenvalue problems has not been systematically developed. Resolving this issue would clarify the approximation and enable a more complete description of conditioned or driven stochastic processes.

References

Third, our moment calculation uses a symplectic reduction of an underlying contact eigenvalue problem. To our knowledge, the variational and geometric structure of such contact eigenvalue problems has not been systematically developed in the large-deviation setting. A more complete treatment would clarify the role of the contact eigenvectors, the accuracy of the reduced approximation used here, and the construction of driven processes that realize atypical fluctuations in supercritical growing systems.

— Large-deviations theory for growing chemical reaction networks  (2609.30970 - Gagrani et al., 25 Sep 2026) in Section Discussion