Scaling limit of Fourier-Walsh coefficients (a framework)

TL;DR

This paper investigates how the Fourier-Walsh spectra of discrete models with independent random signs converge to continuous limits, providing a framework for understanding their scaling behavior.

Contribution

It introduces a framework for analyzing the scaling limits of Fourier-Walsh coefficients in models governed by independent random signs.

Findings

Fourier-Walsh spectra convergence is established under certain conditions.

The framework applies to various discrete models converging to continuous limits.

Provides insights into the spectral behavior of models with independent randomness.

Abstract

Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.