16.12.2008 (Tuesday)

Tuck's incompressibility function: statistics for zeta zeros and eigenvalues

Regular Seminar Michael Berry (Bristol)

16:00 Brunel U.
room M128

Tuck devised a function Q(x), associated with a function D(x), whose positivity guarantees the absence of complex zeros of D(x) close to the real x axis, and observed that large values of Q are very rare if D is associated with the Riemann zeros. In an unusual and challenging application of random-matrix theory with P Shukla, this is explained by studying the probability distribution P(Q) for functions D with N zeros corresponding to eigenvalues of the Gaussian unitary ensemble (GUE).