  The structure of Lyapunov spectra for many particle systems with a random
interaction between the particles is discussed. The dynamics of the tangent
space is expressed as a master equation, which leads to a formula that connects
the positive Lyapunov exponents and the time correlations of the particle
interaction matrix. Applying this formula to one and two dimensional models we
investigate the stepwise structure of the Lyapunov spectra, which appear in the
region of small positive Lyapunov exponents. Long range interactions lead to a
clear separation of the Lyapunov spectra into a part exhibiting stepwise
structure and a part changing smoothly. The part of the Lyapunov spectrum
containing the stepwise structure is clearly distinguished by a wave like
structure in the eigenstates of the particle interaction matrix. The two
dimensional model has the same step widths as found numerically in a
deterministic chaotic system of many hard disks.
