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We shall consider the Schr\"odinger operators on $\mathbf{R}^2$ with random$\delta$ magnetic fields. Under some mild conditions on the positions and thefluxes of the $\delta$-fields, we prove the spectrum coincides with$[0,\infty)$ and the integrated density of states (IDS) decays exponentially atthe bottom of the spectrum (Lifshitz tail), by using the Hardy type inequalityby Laptev-Weidl. We also give a lower bound for IDS at the bottom of thespectrum.

Schr\"odinger operators with random $\delta$ magnetic fields