  We propose to stabilise HMC simulations of lattice QCD with very light Wilson
quarks by splitting the quark determinant into two factors and by treating the
factor that includes the contribution of the low modes of the Dirac operator as
a reweighting factor. In general, determinant reweighting becomes inefficient
on large lattices, because the statistical fluctuations of quark determinants
increase exponentially with the lattice volume. Random matrix theory and some
numerical studies now suggest that the low-mode contribution to the determinant
behaves differently, which allows factorisations to be devised that preserve
the efficiency of the simulation on large lattices.
