Publication

Stochastic Estimates for the Thin-Film Equation with Thermal Noise

2026

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 $d\ge 1$ 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].

Official source

https://infoscience.epfl.ch/entities/publication/0a0700b6-6729-403c-9af2-7b56b09dba9d

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2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0a0700b6-6729-403c-9af2-7b56b09dba9d

About this result

Related concepts (18)

Noise (electronics)

In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects. In particular, noise is inherent in physics and central to thermodynamics. Any conductor with electrical resistance will generate thermal noise inherently. The final elimination of thermal noise in electronics can only be achieved cryogenically, and even then quantum noise would remain inherent. Electronic noise is a common component of noise in signal processing.

Johnson–Nyquist noise

Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment (such as radio receivers) can drown out weak signals, and can be the limiting factor on sensitivity of electrical measuring instruments.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

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Stochastic Estimates for the Thin-Film Equation with Thermal Noise

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