Statistical Mechanics of Self--Gravitating System : Cluster Expansion   Method
  We study statistical mechanics of the self--gravitating system applying the cluster expansion method developed in solid state physics. By summing infinite series of diagrams, we derive a complex free energy whose imaginary part is related to the relaxation time of the system. Summation of another series yields two--point correlation function whose correlation length is essentially given by the Jeans wavelength of the system. 
Osamu Iguchi, Tomomi Kurokawa, Masahiro Morikawa, Akika Nakamichi,   Yasuhide Sota, Takayuki Tatekawa, and Kei--ichi Maeda