Monte Carlo simulations of the disk white dwarf population

In order to understand the dynamical and chemical evolution of our Galaxy it is of fundamental importance to study the local neighborhood. White dwarf stars are ideal candidates to probe the history of the solar neighborhood, since these ``fossil'' stars have very long evolutionary time-scales and, at the same time, their evolution is relatively well understood. In fact, the white dwarf luminosity function has been used for this purpose by several authors. However, a long standing problem arises from the relatively poor statistics of the samples, especially at low luminosities. In this paper we assess the statistical reliability of the white dwarf luminosity function by using a Monte Carlo approach.