  We compute the Fermi velocity of the Dirac quasiparticles in clean graphene
at the charge neutrality point for strong Coulomb coupling alpha_g. We perform
a Lattice Monte Carlo calculation within the low-energy Dirac theory, which
includes an instantaneous, long-range Coulomb interaction. We find a
renormalized Fermi velocity v_FR > v_F, where v_F = c/300. Our results are
consistent with a momentum-independent v_FR which increases approximately
linearly with alpha_g, although a logarithmic running with momentum cannot be
excluded at present. At the predicted critical coupling alpha_gc for the
semimetal-insulator transition due to excitonic pair formation, we find
v_FR/v_F = 3.3, which we discuss in light of experimental findings for v_FR/v_F
at the charge neutrality point in ultra-clean suspended graphene.
