Shu Nakamura Lifshitz tail for 2D discrete Schrodinger operator with random magnetic field (25K, LaTeX2e with AMS-LaTeX macro packages) ABSTRACT. Lifshitz tail for 2 dimensional discrete Schrodinger operator with Anderson-type random magnetic field is proved. We first prove local energy estimates for deterministic discrete magnetic Schrodinger operators, and then follow the large deviation argument of Simon [J. Stat. Phys. 38, 65-76 (1985)]