Particle in a random magnetic field on a plane

We study the properties of a two-dimensional spinless particle moving in a random magnetic field. This problem arises in the context of a modern theory of strongly correlated systems as well as in the theory of vortex-lines dynamics in high-${\mathit{T}}_{\mathit{c}}$ materials. The problem is investigated with a variety of methods including direct perturbation theory, quasiclassical approximation, the method of an optimal fluctuation, and Monte Carlo simulations. We obtain a shape of the density of states near the unrenormalized lower boundary of the spectrum, a particle mobility, and its diamagnetic orbital susceptibility.