Subject of my Diploma Thesis in Theoretical High Energy Physics:

On the Universality of Matrix Models for Random Surfaces

In the thesis, an alternative procedure to eliminate irregular contributions in the perturbation expansion of c=0-matrix models representing the sum over triangulations of random surfaces (which is a model for two dimensional quantum gravity) is presented, thereby reproducing the results of Tutte [1] and Brézin et al. [2] for the planar model.

The advantage of this method is that the universality of the critical exponents can be proven from general features of the model alone without explicit determination of the free energy and therefore allows for several straightforward generalizations including cases with non-vanishing central charge (1 >) c > 0, reperesenting a coupling of 2d quantum gravity to matter fields.

[1] W.T.Tutte, Can.J.Math. 14 (1962) 21
[2] E.Brézin, C.Itzykson, G.Parisi, J.B.Zuber, Commun.Math.Phys. 59 (1978) 35

The related article was published (under my birth name) in Eur.Phys.J.C 8, 523-526 (1999). PostScript or PDF version: here