  We introduce the boson and the fermion point processes from the elementary
quantum mechanical point of view. That is, we consider quantum statistical
mechanics of canonical ensemble for a fixed number of particles which obey
Bose-Einstein, Fermi-Dirac statistics, respectively, in a finite volume.
Focusing on the distribution of positions of the particles, we have point
processes of the fixed number of points in a bounded domain. By taking the
thermodynamic limit such that the particle density converges to a finite value,
the boson/fermion processes are obtained. This argument is a realization of the
equivalence of ensembles, since resulting processes are considered to describe
a grand canonical ensemble of points. Random point processes corresponding to
para-particles of order two are discussed as an application of the formulation.
A statistics of a system of composite particles at zero temperature are also
considered as a model of determinantal random point processes.
