Black hole motion in Euclidean space as a diffusion process
  A diffusion equation for a black hole is derived from the Bunster-Carlip equations. Its solution has the standard form of a Gaussian distribution. The second moment of the distribution determines the quantum of black hole area. The entropy of diffusion process is the same, apart from the logarithmic corrections, as the Bekenstein-Hawking entropy. 
Kostiantyn Ropotenko
gr-qc hep-th