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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.00708 |
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Table of Contents:
- We propose a new type of SPDEs, singular or with regularized noises, motivated by a study of the fluctuation of the density field in a microscopic interacting particle system. They include a large scaling parameter $N$, which is the ratio of macroscopic to microscopic size, and another scaling parameter $K=K(N)$, which controls the formation of the interface of size $K^{-1/2}$ in the density field. They are derived heuristically from the particle system, assuming the validity of the so-called ``Boltzmann-Gibbs principle", that is, a combination of the local ensemble average due to the local ergodicity and its asymptotic expansion. We study a simple situation where the interface is flat and immobile. Under making a proper stretch to the normal direction to the interface, we observe a Gaussian fluctuation of the interface. We also heuristically derive a nonlinear SPDE which describes the fluctuation of the interface.