We study the correlation between the \gamma –ray flux ( F _ { \gamma } ) , averaged over the first 11 months of Fermi survey and integrated above 100 MeV , and the radio flux density ( F _ { r } at 20 GHz ) of Fermi sources associated with a radio counterpart in the AT20G survey .
Considering the blazars detected in both bands , the correlation is highly significant and has the form F _ { \gamma } \propto F _ { r } ^ { 0.85 \pm 0.04 } , similar for BL Lac and FSRQ sources .
However , only a small fraction ( \sim 1/15 ) of the AT20G radio sources with flat radio spectrum , are detected by Fermi .
To understand if this correlation is real , we examine the selection effects introduced by the flux limits of both the radio and \gamma –ray surveys , and the importance of variability of the \gamma –ray flux .
After accounting for these effects , we find that the radio/ \gamma –ray flux correlation is real , but its slope is steeper than the observed one , i.e . F _ { \gamma } \propto F _ { r } ^ { \delta } with \delta in the range 1.25 - 1.5 .
The observed F _ { \gamma } – F _ { r } correlation and the fraction of radio sources detected by Fermi is reproduced assuming a long term \gamma –ray flux variability following a log–normal probability distribution with standard deviation \sigma \geq 0.5 ( corresponding to F _ { \gamma } varying by at least a factor 3 ) .
Such a variability is compatible , even if not necessarily equal , with what observed when comparing , for the sources in common , the EGRET and the Fermi \gamma –ray fluxes ( even if the Fermi fluxes are averaged over \sim 1 year ) .
Another indication of variability is the non detection of 12 out of 66 EGRET blazars by Fermi , despite its higher sensitivity .
We also study the strong linear correlation between the \gamma –ray and the radio luminosity of the 144 AT20G– Fermi associations with known redshift and show , through partial correlation analysis , that it is statistically robust .
Two possible implications of these correlations are discussed : the contribution of blazars to the extragalactic \gamma –ray background and the prediction of blazars that might undergo extremely high states of \gamma –ray emission in the next years .