  We develop statistical mechanics for stochastic growth processes as applied
to Laplacian growth by using its remarkable connection with a random matrix
theory. The Laplacian growth equation is obtained from the variation principle
and describes adiabatic (quasi-static) thermodynamic processes in the
two-dimensional Dyson gas. By using Einstein's theory of thermodynamic
fluctuations we consider transitional probabilities between thermodynamic
states, which are in a one-to-one correspondence with planar domains.
Transitions between these domains are described by the stochastic Laplacian
growth equation, while the transitional probabilities coincide with the
free-particle propagator on the infinite dimensional complex manifold with the
K\"ahler metric.
