An anisotropy parameter h in (0, 1] induces on Qₚ² a duality-compatible, two-scale filtration that collapses to one scale at the right endpoint. This filtration defines shell-uniform transition laws for hierarchical random walks on a discrete group whose scaling limits are Lévy processes on Qₚ². The diffusion constants of the coordinate processes jump at the right endpoint, even though the radial jump law depends continuously on h. This instance of geometry-induced criticality isolates a structural mechanism that should extend to locally compact abelian groups and suggests a route to studying critical behavior in ultrametric models.
Rajkumar et al. (Mon,) studied this question.