English

Large deviations principle for the cubic NLS equation with slowly decaying data

Analysis of PDEs 2025-12-09 v1 Probability

Abstract

In this note, we prove a sharp large derivation principle (LDP) for the cubic nonlinear Schr\"odinger equation with Gaussian random initial data in Fourier Lebesgue spaces. As a consequence, we improve the exponential decay condition in [M.A. Garrido, R. Grande, K.M. Kurianski, G. Staffilani. Commun. Pure Appl. Math. 76 (2023), 4087--4136] to 1\ell^1 decay.

Keywords

Cite

@article{arxiv.2512.07773,
  title  = {Large deviations principle for the cubic NLS equation with slowly decaying data},
  author = {Rui Liang and Yuzhao Wang},
  journal= {arXiv preprint arXiv:2512.07773},
  year   = {2025}
}

Comments

18 pages

R2 v1 2026-07-01T08:15:16.657Z