This chapter presents a theory of homogenisation for random bianisotropic media exhibiting an ergodic structure. It shows that for such a medium there exists a homogenised system of the Maxwell type. To begin, the chapter presents an introduction to the necessary notions from the theory of ergodicity that will be used in this treatment of homogenisation. It then showcases a model for a random complex medium, on which this chapter's analysis will be based. The chapter also details a formal two-scale approach to set ideas and understand the basic mechanisms that will lead to a homogenised system, as well as to identify the coefficients of the homogenised system. Finally, this chapter presents some rigorous results on the homogenisation of random complex electromagnetic media.
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