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Radial Heat Diffusion from the Root of a Homogeneous Tree and the Combinatorics of Paths

Joel M. Cohen; Mauro Pagliacci; Massimo A. Picardello — 2008

Bollettino dell'Unione Matematica Italiana

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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