I read on Wikipedia that a Gaussian process with a Matérn covariance function is $\lfloor\nu\rfloor$ times mean-square differentiable, where $\nu$ is the smoothness parameter of the Matérn covariance function. What can I say about the sample differentiability or continuity (or differentiability or continuity with probability one) of these processes? I guess there are some simple results but I cannot seem to find them...
Edit: I found this Math Overflow answer and these lecture slides, which state that the sample functions from a Gaussian process with a Matérn covariance function are $\lfloor\nu\rfloor - 1$ times differentiable. Unfortunately, the links come without any derivations. Any ideas where to find those?