Finite-size corrections in random matrix theory and Odlyzko's dataset for the Riemann zeros
Peter J Forrester, Anthony Mays
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | ROYAL SOC | Published : 2015
Odlyzko has computed a dataset listing more than 10 successive Riemann zeros, starting from a zero number to beyond 10 . This dataset relates to random matrix theory as, according to the Montgomery-Odlyzko law, the statistical properties of the large Riemann zeros agree with the statistical properties of the eigenvalues of large random Hermitian matrices. Moreover, Keating and Snaith, and then Bogomolny and co-workers, have used N × N random unitary matrices to analyse deviations from this law. We contribute to this line of study in two ways. First, we point out that a natural process to apply to the dataset is to minimize it by deleting each member independently with some specified probabi..View full abstract
This research project is part of the programme of study supported by the ARC Centre of Excellence for Mathematical and Statistical Frontiers.