  We study a simple model of a random walker in d dimensions moving in the
presence of a local heterogeneous attracting factor expressed in terms of an
assigned space-dependent "attractiveness function", a situation frequently
encountered in the study of various diffusion problems. The corresponding
drift-diffusion equation and the explicit expressions for the velocity field
and the diffusion coefficient are obtained and discussed. We consider some
examples of applications of the results obtained to chemotactic diffusion
processes and social dynamics.
