Diffusion processes with ultrametric jumps

In the theory of spin glasses the relaxation processes are modelled by random jumps in ultrametric spaces. One may argue that at the border of glassy and nonglassy phases the processes combining diffusion and jumps may be relevant. Using the Dirichlet form technique we construct a model of diffusion on the real line with jumps on the Cantor set. The jumps preserve the ultrametric feature of a random process on unit ball of 2-adic numbers.