Diffusion on $κ$-Minkowski space

We study the spectral dimension associated with diffusion processes on Euclidean $κ$-Minkowski space. We start by describing a geometric construction of the "Euclidean" momentum group manifold related to $κ$-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 behaviours for the spectral dimension according to the choice of deformed Laplacian, from dimensional reduction to super-diffusion.

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