  In this paper we study the stochastic homogenisation of free-discontinuity
functionals. Assuming stationarity for the random volume and surface
integrands, we prove the existence of a homogenised random free-discontinuity
functional, which is deterministic in the ergodic case. Moreover, by
establishing a connection between the deterministic convergence of the
functionals at any fixed realisation and the pointwise Subadditive Ergodic
Theorem by Akcoglou and Krengel, we characterise the limit volume and surface
integrands in terms of asymptotic cell formulas.
