Stochastic Estimates for the Thin-Film Equation with Thermal Noise
Abstract
Abstract We construct and derive uniform stochastic estimates on the renormalised model for a class of fourth-order conservative quasilinear singular SPDEs in arbitrary dimension $$d\ge 1 $$ d ≥ 1 and in the full subcritical regime of noise regularity. The prototype of the class of equations we study is the so-called thin-film equation with thermal noise, also commonly referred to in the literature as the stochastic thin-film equation. We derive an explicit expression for the form of the counterterm as a function of the film mobility which is in surprising agreement with the form conjectured in [GGKO23, Remark 9.1].
Fields of Study & Subjects
Stochastic processes and financial applications
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
Publication details
- Journal / source
- Communications in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 407
- Issue
- 9
- Publication date
- 1 August 2026
- Language
- EN