Ultrametric diffusion in a strong centrally symmetric field

A random process at the boundary of a finite regularly branching tree encapsulated in the central-symmetric external field is considered with respect to introduced ultrametricity. We demonstrate an explicit procedure of reduction of dimensionality of the problem. In addition, we consider the strong-field-limit and show that in this case the problem can be solved exactly. The exact solution of the strong-field-limit problem related to the case of linearly growing hierarchy of barriers is exemplified and supplemented by estimations of the transition kinetics into the ground state.