Probability Distribution Function of the Coarse-grained Scalar Field at   Finite Temperature
  We present a formalism to calculate the probability distribution function of a scalar field coarse-grained over some spatial scales with a Gaussian filter at finite temperature. As an application, we investigate the role of subcritical fluctuations in the electroweak phase transition in the minimal standard model. It is concluded that the universe was in a mixed state of true and false vacua already at the critical temperature. 
Masahide Yamaguchi and Jun'ichi Yokoyama