Title of my Master's Thesis in Theoretical High Energy Physics:

On the Universality of Matrix Models for Random Surfaces


Matrix models are a mathematical device to represent the sum over triangulations of random surfaces, a model for 2-dimensional quantum gravity. In the thesis, an alternative procedure to eliminate irregular contributions in the perturbation expansion of c=0-matrix models is derived that reproduces the results of Tutte [1] and Brézin et al. [2] for the planar model.

The advantage of the new procedure 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. It therefore allows for several straightforward generalizations including cases with non-vanishing central charge c, 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

An article on the topic was published in European Physical Journal C 8, 523-526 (1999). Free PostScript and PDF version: here