Cohen, Joel M. and Pagliacci, Mauro and Picardello, Massimo A.:
Radial Heat Diffusion from the Root of a Homogeneous Tree and the Combinatorics of Paths
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.3, p. 619-628, (English)
pdf (371 Kb), djvu (98 Kb). | MR 2455335 | Zbl 1192.80004
Sunto
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 $\Delta + c \frac{\partial}{\partial r}$ for some constant $c$ that represents a drift towards (or away from) the origin.
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