Numerical simulation of random Dirac operators

A Riemannian manifold can be described without loss of information by a spectral triple (A,H,D), where H is a Hilbert space, A is a (commutative) algebra with a representation in H and D is a Dirac operator acting on H. The spectral triple, however, also allows for an extension of the notion of geometry: by considering a spectral triple with a non-commutative algebra, one obtains a so-called non-commutative geometry.
A class of non-commutative geometries known as fuzzy spaces is introduced, and their behaviour when the Dirac operator is allowed to fluctuate according to a certain probability measure is investigated by means of Markov chain Monte Carlo integration.