The theoretical description is presented for long range
correlations of observables measured for distant rapidity
intervals in nucleus-nucleus interactions at high energy.
For the hard region in the scope of QCD perturbative approach
the two-particle inclusive cross sections for parton creation
with large transverse momentum are calculated taking into account
multiple rescattering. The obtained values of cross sections
are used to estimate numerically the correlation coefficients
for jets numbers in distant rapidity intervals.
In the soft region we obtained (using the quark-gluon strings fusion
model) the correlation functions and correlation coefficients
for transverse momenta and multiplicities of particles created
in different rapidity intervals. The dependence of these
correlations on energy and impact parameter is studied.
We investigated the correlations between the mean values of
transverse momenta for particles created in different rapidity
intervals. It is demonstrated that for heavy nuclea these
correlations do not tend to zero contrary to the correlations
of transverse momenta of particles with different rapidity
intervals. The restrictions induced by the real experimental
conditions are also studied. Applying the strings fusion model
the correlations of multiplicity and transverse momentum are
fitted using the NA49 experimental results taking into account
the specific features of the installation and events selection
method.