Diffusion on κ-Minkowski space

We study the spectral dimension associated with diffusion processes on Euclidean kappa-Minkowski space. We start by describing a geometric construction of the Euclidean momentum group manifold related to kappa-Minkowski space. On such space we identify various candidate Laplacian functions, i.e. deformed Casimir invariants, and calculate the corresponding spectral dimension for each case. The results obtained show a variety of running behaviors for the spectral dimension according to the choice of deformed Laplacian, from dimensional reduction to superdiffusion.