Heat kernel and Green function estimates on affine buildings of type $\tilde{A}_r$

Details Heat kernel and Green function estimates on affine buildings of type $\tilde{A}_r$ Heat kernel and Green function estimates on affine buildings of type $\tilde{A}_r$

2006-12-14

arxiv.org/abs/math/0612385v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We obtain a global estimate of the transition density $p^n(0,x)$ associated
to a nearest neighbor random walk, called here "simple", on affine buildings of
type $\widetilde{A}_r$. Then we deduce a global estimate of the Green function.
This is the analogue of a result on Riemannian symmetric spaces of the
noncompact type.

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