Wednesday, November 28, 2018 - 16:15 in V3-201
The level spacing distribution at the hard edge
A talk in the AG Zufallsmatrizen series by
Valentin Gorski from Bielefeld University
| Abstract: |
The level spacing distribution in the bulk of a spectrum is approximately given by the Wigner surmise. Yet, at the hard and the soft edge one can expect strong deviations from these laws. Using the orthogonal polynomial method we derive the spacing distribution of the smallest two singular values of the chiral Gaussian unitary ensemble (chGUE) at finite matrix dimension with additional characteristical polynomials in the weight. The number of these polynomials represents the number of flavors (types of quarks) in the physical system. This ensemble approximates the Euclidean Dirac operator in Quantum Chromodynamics
QCD). In my talk, I will report on the behavior of the level spacing distribution in this particular setting.
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