  The Fermi-LAT observational data of the diffuse $\gamma$ ray emission from
the Large Magellanic Cloud (LMC), were examined to test for the existence of
underlying long range correlations. A statistical test applied to the data
indicated that the probability that data are random is $\sim 10^{-99}$. Thus we
proceeded and have used the counts-number data to compute 2D spatial
autocorrelation, power spectrum, and structure function.
  The most important result of the present study is a clear indication for
large scale spatial underlying correlations. This is evident in {\bf all} the
functions mentioned above. The 2D power spectrum has a logarithmic slope of -3
on large spatial scales and a logarithmic slope of -4 on small spatial scales.
The structure function has logarithmic slopes equaling 1 and 2 for the large
and small scales respectively. The logarithmic slopes of the structure function
and the power spectrum are consistent.
  A plausible interpretation of these results is the existence of a large scale
{\it compressible turbulence} with a 3D logarithmic slope of -4 extending over
the entire extent of the LMC. This may reflect the fact that the $\gamma$ Ray
emission is in star forming regions, where jets and shocks are abundant.
  Both the power spectrum and structure function exhibit steeper logarithmic
slopes for smaller spatial scales. This is interpreted as an indication that
the turbulent region has an effective depth of about 1.5 kpc.
