  Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic
strings, may have a profound physical meaning in terms of dynamical models of
vacuum fluctuations in stochastically quantized field theories. Here we present
analytic results for the invariant density of chaotic strings, as well as for
the coupling parameter dependence of given observables of the chaotic string
such as the vacuum expectation value. A highly nontrivial and selfsimilar
parameter dependence is found, produced by perturbative and nonperturbative
effects, for which we develop a mathematical description in terms of suitable
scaling functions. Our analytic results are in good agreement with numerical
simulations of the chaotic dynamics.
