What question did this study set out to answer?

This work aims to develop a deeper understanding of persistence time distributions in open metastable systems through analytic methods.

February 21, 2026Open Access

Structural Origins of Exponential Persistence III (SOEP)

Key Points

This work aims to develop a deeper understanding of persistence time distributions in open metastable systems through analytic methods.
Developing spectral dimensional reduction discussed in SOEP II.
Proving persistence densities through Laplace transform representations.
Applying analytic continuation and contour deformation techniques.
Utilizing saddle-point analysis and cumulant-based Edgeworth expansions.
Identified that persistence distributions depend on dominant spectral eigenvalues.
Derived explicit exponential asymptotics with controlled remainder bounds.
Established a framework for universality classification under renormalization.

Abstract

Structural Origins of Exponential Persistence III (SOEP) develops the analytic asymptotic structure of persistence time distributions in open metastable systems. Building on the spectral dimensional reduction established in SOEP II, the work proves that persistence densities admit Laplace transform representations dominated by isolated slow spectral poles. Using analytic continuation, contour deformation, saddle-point analysis, and cumulant-based Edgeworth expansions, explicit exponential asymptotics with controlled remainder bounds are derived. The results show that persistence distributions asymptotically depend only on dominant spectral eigenvalues and finite cumulant structure, providing analytic closure for the spectral persistence reduction and preparing the foundation for universality classification under renormalization. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/

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