  The study of quantum quasi-particles at low temperatures including their
statistics, is a frontier area in modern physics. In a seminal paper F.D.
Haldane proposed a definition based on a generalization of the Pauli exclusion
principle for fractional quantum statistics. The present paper is a study of
quantum quasi-particles obeying Haldane statistics in a fully non-linear
kinetic Boltzmann equation model with large initial data on a torus. Strong L1
solutions are obtained for the Cauchy problem. The main results concern
existence, uniqueness and stability. Depending on the space dimension and the
collision kernel, the results obtained are local or global in time.
