While federated learning is a promising approach for training deep learning models over distributed sensitive datasets, it presents new challenges for machine learning, especially when applied in the medical domain where multi-centric data heterogeneity is common. Building on previous domain adaptation works, this paper proposes a novel federated learning approach for deep learning architectures via the introduction of local-statistic batch normalization (BN) layers, resulting in collaboratively-trained, yet center-specific models. This strategy improves robustness to data heterogeneity while also reducing the potential for information leaks by not sharing the center-specific layer activation statistics. We benchmark the proposed method on the classification of tumorous histopathology image patches extracted from the Camelyon16 and Camelyon17 datasets. We show that our approach compares favorably to