Quantum field theory for discrepancies II: 1/N corrections using fermions

TL;DR

This paper develops a fermionic approach to compute 1/N corrections in quantum field theory for discrepancies, providing explicit diagrammatic expansions and first-order results for certain discrepancy measures.

Contribution

It introduces a fermionic variable method to calculate 1/N corrections in discrepancy probability distributions, extending previous work with explicit diagrammatic expansions.

Findings

Derived 1/N corrections using fermionic variables

Provided second-order diagrammatic expansion

Explicit first-order expansion for specific discrepancies

Abstract

We calculate the 1/N corrections to the probability distributions of quadratic discrepancies for sets of N random points. This is achieved by the introduction of fermionic variables. We give the diagrammatic expansion up to and including the second order in 1/N. For some discrepancies, we give the explicit expansion to first order.