01002nas a2200133   4500008004100000245006100041210006000102520056900162100002200731700002100753700001900774700002700793856004800820       2018                        en  d00aStochastic homogenisation of free-discontinuity problems0 aStochastic homogenisation of freediscontinuity problems3 aIn 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.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida  uhttp://preprints.sissa.it/handle/1963/35309