# A Wong-Zakai theorem for the stochastic mass critical NLS

## TL;DR

This paper establishes a Wong-Zakai theorem for the stochastic mass-critical nonlinear Schrödinger equation, addressing the convergence of solutions under approximations of stochastic noise in a dispersive PDE setting.

## Contribution

It provides the first Wong-Zakai type result for the mass-critical stochastic NLS, highlighting key differences from SDEs and parabolic SPDEs.

## Key findings

- Proves convergence of solutions under noise approximation
- Identifies key subtleties in dispersive stochastic PDEs
- Differentiates between large-n and limiting cases

## Abstract

We prove a Wong-Zakai theorem for the defocusing mass-critical stochastic nonlinear Schr\"odinger equation (NLS) on $\mathbb{R}$. The main ingredient are careful mixtures of bootstrapping arguments at both deterministic and stochastic levels. Several subtleties arising from the proof mark the difference between the dispersive case and corresponding situations in SDEs and parabolic stochastic PDEs, as well as the difference between the large-$n$ case and the limiting ($n=\infty$) case.