Tuck's incompressibility function: statistics for zeta zeros and eigenvalues
| dc.creator | Berry, M V | |
| dc.creator | Shukla, P | |
| dc.date | 2008-07-22 | |
| dc.date.accessioned | 2026-07-07T09:52:06Z | |
| dc.date.available | 2026-07-07T09:52:06Z | |
| dc.description | For any function that is real for real x, positivity of Tuck's function Q(x)=D'^2(x)/(D'^2(x)-D"(x) D(x)) is a condition for the absence of the complex zeros close to the real axis. Study of the probability distribution P(Q), for D(x) with N zeros corresponding to eigenvalues of the Gaussian unitary ensemble (GUE), supports Tuck's observation that large values of Q are very rare for the Riemann zeros. P(Q) has singularities at Q=0, Q=1 and Q=N. The moments (averages of Q^m) are much smaller for the GUE than for uncorrelated random (Poisson-distributed) zeros. For the Poisson case, the large-N limit of P(Q) can be expressed as an integral with infinitely many poles, whose accumulation, requiring regularization with the Lerch transcendent, generates the singularity at Q=1, while the large-Q decay is determined by the pole closest to the origin. Determining the large-N limit of P(Q) for the GUE seems difficult. | |
| dc.description | 40 Pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0807.3474 | |
| dc.identifier | http://arxiv.org/abs/0807.3474 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165474 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.subject | Mathematical Physics | |
| dc.title | Tuck's incompressibility function: statistics for zeta zeros and eigenvalues | |
| dc.type | text |