  Quantization and asymptotic behaviour of a variant of discrete random walk on
integers are investigated. This variant, the $\epsilon_{V^{k}}$ walk, has the
novel feature that it uses many identical quantum coins keeping at the same
time characteristic quantum features like the quadratically faster than the
classical spreading rate, and unexpected distribution cutoffs. A weak limit of
the position probability distribution (pd) is obtained, and universal
properties of this arch sine asymptotic distribution function are examined.
Questions of driving the walk are investigated by means of a quantum optical
interaction model that reveals robustness of quantum features of walker's
asymptotic pd, against stimulated and spontaneous quantum noise on the coin
system.
