  Kernel methods, being supported by a well-developed theory and coming with
efficient algorithms, are among the most popular and successful machine
learning techniques. From a mathematical point of view, these methods rest on
the concept of kernels and function spaces generated by kernels, so called
reproducing kernel Hilbert spaces. Motivated by recent developments of learning
approaches in the context of interacting particle systems, we investigate
kernel methods acting on data with many measurement variables. We show the
rigorous mean field limit of kernels and provide a detailed analysis of the
limiting reproducing kernel Hilbert space. Furthermore, several examples of
kernels, that allow a rigorous mean field limit, are presented.
