  We discuss the behavior of the largest Lyapunov exponent $\lambda$ in the
incoherent phase of large ensembles of heterogeneous, globally-coupled, phase
oscillators. We show that the scaling with the system size $N$ depends on the
details of the spacing distribution of the oscillator frequencies. For
sufficiently regular distributions $\lambda \sim 1/N$, while for strong
fluctuations of the frequency spacing, $\lambda \sim \ln N/N$ (the standard
setup of independent identically distributed variables belongs to the latter
class). In spite of the coupling being small for large $N$, the development of
a rigorous perturbative theory is not obvious. In fact, our analysis relies on
a combination of various types of numerical simulations together with
approximate analytical arguments, based on a suitable stochastic approximation
for the tangent space evolution. In fact, the very reason for $\lambda$ being
strictly larger than zero is the presence of finite size fluctuations. We trace
back the origin of the logarithmic correction to a weak synchronization between
tangent and phase space dynamics.
