Discrepancy theory

Discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure-theoretic and combinatorial settings. Just as Ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity.

A significant event in the history of discrepancy theory was the 1916 paper of Weyl on the uniform distribution of sequences in the unit interval.

Theorems

Discrepancy theory is based on the following classic theorems:

• Geometric discrepancy theory
• The theorem of van Aardenne-Ehrenfest
• Arithmetic progressions (Roth, Sarkozy, Beck, Matousek & Spencer)
• Beck–Fiala theorem
• Six Standard Deviations Suffice (Spencer)