Graphons arising from graphs definable over finite fields

TL;DR

This paper extends Tao's algebraic regularity lemma to asymptotic classes and applies it to analyze expander difference polynomials over finite fields with Frobenius powers.

Contribution

It introduces a version of the algebraic regularity lemma for asymptotic classes and explores its application to graphons derived from finite field graphs.

Findings

Established a regularity lemma for asymptotic classes

Analyzed expander difference polynomials over finite fields

Connected graphons to algebraic structures in finite fields

Abstract

We prove a version of Tao's algebraic regularity lemma for asymptotic classes in the context of graphons. We apply it to study expander difference polynomials over fields with powers of Frobenius.