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 Δ + c ∂/∂r for some constant c that represents a drift towards (or away from) the origin.
Cohen, J.m., Pagliacci, M., Picardello, A.m. (2008). Radial heat diffusion from the root of a homogeneous tree and the combinatorics of paths. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1(3), 619-628.
Radial heat diffusion from the root of a homogeneous tree and the combinatorics of paths
PICARDELLO, ANGELO MASSIMO
2008-01-01
Abstract
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 Δ + c ∂/∂r for some constant c that represents a drift towards (or away from) the origin.File in questo prodotto:
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