Year: 2013
Type: preprint
Abstract: We study sequences of functions of the form F_p^n -> {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 are also able to 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 Szegedy in [Sze10].
Source: arXiv (Cornell University)
Authors: Hatami, Hamed, Hatami, Pooya, Hirst, James
Institutions: McGill University, University of Chicago
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4293497216