Radial Heat Diffusion from the Root of a Homogeneous Tree and the Combinatorics of Paths
We compute recursively the heat semigroup in a rooted homogeneous tree for the diffusion with radial (with respect to the root) but non-isotropic transition probabilities. This is the discrete analogue of the heat operator on the disc given by for some constant that represents a drift towards (or away from) the origin.