  We consider a stochastic Laplacian growth problem in the framework of normal
random matrices. In the large $N$ limit the support of eigenvalues of random
matrices is a planar domain with a sharp boundary which evolves under a change
in the size of matrices. This evolution can be interpreted as a stochastic
growth process. We show that the most probable growth scenario is similar to
deterministic Laplacian growth. The other scenarios involve Laplacian growth in
the presence of fluctuations. We use the random matrix approach to determine a
probability distribution function of fluctuations. The partition function of
fluctuations is shown to be universal. It does not depend on the shape of the
initial domain and depends on the strength of fluctuations and the geometry of
the problem only.
