  The discrete time quantum walk defined as a quantum-mechanical analogue of
the discrete time random walk have recently been attracted from various and
interdisciplinary fields. In this review, the weak limit theorem, that is, the
asymptotic behavior, of the one-dimensional discrete time quantum walk is
analytically shown. From the limit distribution of the discrete time quantum
walk, the discrete time quantum walk can be taken as the quantum dynamical
simulator of some physical systems.
