Discrepancy of random graphs and hypergraphs

TL;DR

This paper determines the discrepancy between two random k-uniform hypergraphs, providing a precise understanding of their structural differences up to a constant factor depending on k.

Contribution

It offers a strong form answer to a question by Bollobás and Scott, establishing the discrepancy for random hypergraphs.

Findings

Discrepancy between two random hypergraphs is determined up to a constant factor.

Provides a precise quantitative measure of hypergraph discrepancy.

Answers a previously open question in hypergraph discrepancy theory.

Abstract

Answering in a strong form a question posed by Bollob\'as and Scott, in this paper we determine the discrepancy between two random k-uniform hypergraphs, up to a constant factor depending solely on k.