  We study the distribution of the eigenvalues of the area operator in loop
quantum gravity concentrating on the part of the spectrum relevant for isolated
horizons. We first show that the approximations relying on integer partitions
are not sufficient to obtain the asymptotic behaviour of the eigenvalue
distribution for large areas. We then develop a method, based on Laplace
transforms, that provides a very accurate solution to this problem. The
representation that we get is valid for any area and can be used to obtain its
asymptotics in the large area limit.
