  We study the spectral properties of the dilute Wigner random real symmetric
n-dimensional matrices H such that the entries H(i,j) take zero value with
probability 1-p/n. We prove that under rather general conditions on the
probability distribution of H(i,j) the semicircle law is valid for the dilute
Wigner ensemble in the limit of infinite n and p. In the second part of the
paper we study the leading term of the correlation function of the resolvent
G(z) of H with large enough Im z in the limit of infinite n and p such that 3/5
log n <log p < log n. We show that this leading term, when considered on the
local spectral scale, converges to the same limit as that of the resolvent
correlation function of the Wigner ensemble of random matrices. This shows that
the moderate dilution of the Wigner ensemble does not alter its universality
class.
