Quantum field theory for discrepancies
A. van Hameren, R. Kleiss
TL;DR
This paper introduces a novel approach using quantum field theory techniques to analyze the probability distribution of discrepancies in point sets, bridging discrepancy theory and quantum physics methods.
Contribution
It applies quantum field theory to compute the probability density of discrepancies, offering new analytical tools for discrepancy analysis.
Findings
Path integrals can model discrepancy distributions
Perturbative methods provide approximate solutions
Non-perturbative analysis reveals deeper properties
Abstract
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem of calculating the probability density of (quadratic) discrepancies into that of evaluating certain path integrals. Both their perturbative and non-perturbative properties are discussed.
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