  In the study of chaotic behaviour of systems of many hard spheres, Lyapunov
exponents of small absolute value exhibit interesting characteristics leading
to speculations about connections to non-equilibrium statistical mechanics.
Analytical approaches to these exponents so far can be divided into two groups,
macroscopically oriented approaches, using kinetic theory or hydrodynamics, and
more microscopically oriented random-matrix approaches in quasi-one-dimensional
systems. In this paper, I present an approach using random matrices and weak
disorder expansion in an arbitrary number of dimensions. Correlations between
subsequent collisions of a particle are taken into account. It is shown that
the results are identical to those of a previous approach based on an extended
Enskog-equation. I conclude that each approach has its merits, and provides
different insights into the approximations made, which include the
Sto{\ss}zahlansatz, the continuum limit, and the long-wavelength approximation.
The comparison also gives insight into possible connections between Lyapunov
exponents and fluctuations.
