Recent works have shown the equivalence between training infinitely wide fully connected neural networks (FCNs) by gradient descent and kernel regression with the Neural Tangent Kernel (NTK). This kernel can also be extended to convolutional neural networks (CNNs), modern architectures that achieve stellar performance in image recognition, and other translational-invariant pattern detection tasks. The resulting Convolutional NTKs have been shown to perform strongly in classification experiments. Still, we lack a quantitative understanding of the generalization capabilities of these models. In this thesis, we introduce a minimal convolutional architecture, and we compute the associated NTK. Following recent works on the statistical mechanics of generalization in kernel methods, we study this kernel's performance in a teacher-student setting, comparing it with the NTK of a two-layer FCN when learning translational-invariant data.