  The density matrix of Hawking radiation is calculated in the model of black
hole with fluctuating horizon. Quantum fluctuations smear the classical horizon
of black hole and modify the density matrix of radiation producing the
off-diagonal elements. The off-diagonal elements may store information of
correlations between radiation and black hole. The smeared density matrix was
constructed by convolution of the density matrix calculated with the
instantaneous horizon with the Gaussian distribution over the instantaneous
horizons. The distribution has the extremum at the classical radius of the
black hole and the width of order of the Planck length. Calculations were
performed in the model of black hole formed by the thin collapsing shell which
follows a trajectory which is a solution of the matching equations connecting
the interior and exterior geometries.
