  We develop a framework for multiscale analysis of elliptic operators with
high-contrast random coefficients. For a general class of such operators, we
provide a detailed spectral analysis of the corresponding homogenised limit
operator. By combining stochastic techniques with operator theory, we link
objects defined on an abstract probability space to their counterparts in the
physical space. In particular, we show that the key characteristics of the
limit operator can be obtained from a single "typical" realisation in the
physical space. Under some lenient assumptions on the configuration of the
random inclusions, we fully characterise the limit of the spectra of the
high-contrast operators in question, which unlike in the periodic setting is
shown to be different to the spectrum of the homogenised operator. Introducing
a new notion of statistically relevant limiting spectrum, we describe the
connection between these two sets.
