  We consider a boson gas on the stretched horizon of the Schwartzschild and
Kerr black holes. It is shown that the gas is in a Bose-Einstein condensed
state with the Hawking temperature $T_c=T_H$ if the particle number of the
system be equal to the number of quantum bits of space-time $ N \simeq
{A}/{{\l_{p}}^{2}}$. Entropy of the gas is proportional to the area of the
horizon $(A)$ by construction. For a more realistic model of quantum degrees of
freedom on the horizon, we should presumably consider interacting bosons
(gravitons). An ideal gas with intermediate statistics could be considered as
an effective theory for interacting bosons. This analysis shows that we may
obtain a correct entropy just by a suitable choice of parameter in the
intermediate statistics.
