  Recently, a theory for artificial magnetism in two-dimensional photonic
crystals has been developed for large wavelength using homogenization
techniques. In this paper we pursue this approach within a rigorous stochastic
framework: dielectric parallel nanorods are randomly disposed, each of them
having, up to a large scaling factor, a random permittivity \epsilon(\omega)
whose law is represented by a density on a window \Delta=[a,b]x[0,h] of the
complex plane. We give precise conditions on the initial probability law
(permittivity, radius and position of the rods) under which the homogenization
process can be performed leading to a deterministic dispersion law for the
effective permeability with possibly negative real part.
  Subsequently a limit analysis h->0, accounting a density law of \epsilon,
which concentrates on the real axis, reveals singular behavior due to the
presence of resonances in the microstructure.
