Archive for Rational Mechanics and Analysis· 2026Q1
A Convergence Result for a Planning Problem for Mean Field Games and Rigorous Proof of a Ventcel–Freidlin-Type Large Deviations Principle for the $$1+1$$ KPZ Equation
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- Q1SCImago
- 2026year
Short summary
A novel connection is established between a singular optimal transport problem for mean field games and a large deviation principle for the KPZ equation, proving a limit for a singular approximate problem and rigorously justifying existing informal analysis.
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Key points
- Connects a singular optimal transport problem (mean field games) with the KPZ equation's large deviation principle.
- Proves a limit for a singular approximate problem with vanishing diffusive flux and relaxed initial condition.
- Offers rigorous justification for informal large deviation analysis of the KPZ equation.
- Addresses planning problems in mean field games and gases with negative pressure.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We study an innovative connection between a very singular optimal transport variational problem with a congestion term connecting two Dirac measures, which is related to the planning problem in mean field games or gases with negative pressure, and a large deviation principle for the KPZ equation. The main result proves a limit of a singular approximate problem with vanishing diffusive flux and a relaxed initial condition. The paper also provides a rigorous justification for the informal analysis of the ad hoc large deviation principle for the KPZ equation appearing in the physics literature.
The authors' abstract, as published at the source. Archive for Rational Mechanics and Analysis, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics