ar X iv : m at h - ph / 0 41 20 17 v 1 7 D ec 2 00 4 Introduction to the Random Matrix Theory : Gaussian Unitary Ensemble and Beyond

ar X iv : 0 90 3 . 54 50 v 1 [ m at h - ph ] 3 1 M ar 2 00 9 On an average over the Gaussian Unitary Ensemble ∗

We study the asymptotic limit for large matrix dimension N of the partition function of the unitary ensemble (β = 2) with weight w(x) := exp − z 2 2x 2 + t x − x 2 2. We compute the leading order term of the partition function and of the coefficients of its Taylor expansion. Our results are valid in the region c 1 N − 1 2 < z < c 2 N 1 4. Such partition function contains all the information on ...

ar X iv : h ep - l at / 0 01 20 10 v 1 7 D ec 2 00 0 1 The Vacuum Polarization : Power Corrections beyond OPE ? ∗

X iv :h ep -l at /0 01 20 10 v1 7 D ec 2 00 0 1 The Vacuum Polarization: Power Corrections beyond OPE ? ∗ M. Göckeler, R. Horsley, W. Kürzinger, V. Linke, D. Pleiter, P. E. L. Rakow and G. Schierholz Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany Deutsches Elektronen-Synchrotron DESY & NIC, D-15735 Zeuthen, Germany Institut für Physik, Humboldt-Universität...

ar X iv : m at h - ph / 0 41 10 85 v 6 2 0 D ec 2 00 4 An Ambiguous Statement Called ‘ Tetrad Postulate ’ and the Correct Field Equations

ar X iv : m at h - ph / 0 41 20 85 v 1 2 3 D ec 2 00 4 Dynamics of Triangulations

We study a few problems related to Markov processes of flipping triangulations of the sphere. We show that these processes are ergodic and mixing, but find a natural example which does not satisfy detailed balance. In this example, the expected distribution of the degrees of the nodes seems to follow the power law d −4 .

ar X iv : m at h - ph / 0 51 20 42 v 1 1 2 D ec 2 00 5 QUANTUM STOCHASTIC POSITIVE EVOLUTIONS : CHARACTERIZATION , CONSTRUCTION , DILATION

A characterization of the unbounded stochastic generators of quantum completely positive flows is given. This suggests the general form of quantum stochastic adapted evolutions with respect to the Wiener (diffusion), Poisson (jumps), or general Quantum Noise. The corresponding irreversible Heisenberg evolution in terms of stochastic completely positive (CP) maps is constructed. The general form...