Limits of Boolean functions on \(\mathbb{F}_p^n\)
type: Item
instance of: scholarly article
title: Limits of Boolean functions on \(\mathbb{F}_p^n\)
zbMATH Open document ID: 1364.11152
author: Hamed Hatami
author: Pooya Hatami
author: James Hirst
published in: The Electronic Journal of Combinatorics
publication date: 2014-10-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1308.4108
full work available at URL: v21i4p2
review text: Summary: We study sequences of functions of the form \(\mathbb{F}_p^n \to \{0,1\}\) for varying \(n\), and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a recently proven equi-distribution theorem from higher order Fourier analysis, we prove that the limits of such convergent sequences can be represented by certain measurable functions. We also show that every such limit object arises as the limit of some sequence of functions. These results are in the spirit of similar results which have been developed for limits of graph sequences. A more general, albeit substantially more sophisticated, limit object was recently constructed by \textit{Balázs Szegedy} [Gowers norms, regularization and limits of functions on abelian groups. 2010. \url{arXiv:1010.6211}].
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 06E30
Mathematics Subject Classification ID: 11B30
zbMATH DE Number: 6360677
zbMATH Keywords: higher order Fourier analysis
zbMATH Keywords: limit theory
MaRDI profile type: Publication
arXiv ID: 1308.4108
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description: scientific article; zbMATH DE number 6360677