  We investigate the effect of the resummation of collinear double logarithms
in the BFKL gluon Green function using the Monte Carlo event generator BFKLex.
The resummed collinear terms in transverse momentum space were calculated in
Ref. [1] and correspond to the addition to the NLO BFKL kernel of a Bessel
function of the first kind whose argument contains the strong coupling and a
double logarithm of the ratio of the squared transverse momenta of the
reggeized gluons. We discuss how these additional terms improve the collinear
convergence of the whole approach and reduce the asymptotic growth with energy
of cross sections. Taking advantage of the Monte Carlo implementation, we show
how the new results reduce the diffusion of the gluon ladder into infrared and
ultraviolet transverse momentum scales, while strongly affecting final state
configurations by reducing the mini-jet multiplicity.
