  We explore the effect of single-particle level fluctuations on the Stoner
instability in a QD with a strong spin-orbit coupling in the framework of the
universal Hamiltonian with the Ising exchange interaction. We reduce the
problem to studying the statistics of extrema of a certain Gaussian process and
demonstrate that, in spite of the randomness of the single-particle levels, the
longitudinal spin susceptibility and all its moments diverge simultaneously at
the point of the Stoner instability which is determined by the standard
criterion involving the mean level spacing only.
