A card from a free library — ask anything, no account, works offline. Every card carries its source.
Zeta zeros and the lattice Dirac operator share GUE statistics
joint
The nearest-neighbour spacings of the zeros of zeta follow the Gaussian Unitary Ensemble of random matrix theory (Montgomery's pair correlation, 1973; Odlyzko's computation, 1987), and so does the low-lying spectrum of the Dirac operator in lattice gauge theory (chiral random matrix theory, Verbaarschot 1994). Hilbert and Polya's reading - the zeros as eigenvalues of an operator - is the same sentence from the other side (Berry-Keating 1999). The Riemann stick sealed the GUE fit on Odlyzko's first 10,000 zeros.
source
Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)
card id
card_joint_gue_statistics
address
WIT.codex.EXP/zeta-zeros-and-the-lattice-dirac-operator-share-/REF.WITNESSED@narrow-highway-the-mille
adjoining cards
- part of → The Millennium floor - seven open questions, and where they connect — a joint that is proven or observed - a part of the floor
- connects at → The Riemann hypothesis — Zeta zeros and the lattice Dirac operator share GUE statistics. montgomery 1973; odlyzko 1
- connects at → Yang-Mills existence and the mass gap — Zeta zeros and the lattice Dirac operator share GUE statistics. montgomery 1973; odlyzko 1
- cites → H. L. Montgomery 1973 — The pair correlation of zeros of the zeta function — the record the joint stands on
- cites → A. M. Odlyzko 1987 — On the distribution of spacings between zeros of the zeta function — the record the joint stands on
- cites → J. J. M. Verbaarschot 1994 — Spectrum of the QCD Dirac operator and chiral random matrix theory — the record the joint stands on
- cites → M. V. Berry 1999 — The Riemann zeros and eigenvalue asymptotics — the record the joint stands on
Is this card incomplete? Tell the library — it will call out for more ↗