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We establish a global-local ergodic theorem about subadditive processes which seems to be a flexible tool to identify some limit problems in homogenization involving several small parameters. When the subadditive process is parametrized in a separable space, we show that the convergence takes place in the variational sense of the epiconvergence (or r-convergence). Some applications are given in the setting of nonlinear elasticity.

Global-Local subadditive ergodic theorems and application to homogenization in elasticity