I will describe the asymptotic behaviour of $L^p$-norms of caloric functions $u$ on affine buildings for compactly supported initial datum $f$. To do so we introduce a mass $M_p(f)$ and show that

I will describe the asymptotic behaviour of the $L^p$-norms of caloric functions $u$ on affine buildings, arising from compactly supported initial datum $f$. To this end, we introduce a mass $Mp​(f)$ and show that...

\[

||k_n||_{\ell^p}^{-1} ||u_n - M_p(f) k_n ||_{\ell^p} -> 0

\]

as $n$ tends to infinity, where $k_n$ is $n$-transition function (heat kernel). It is non-archimedean counterpart to the results obtained by Anker-Papageorgiou-Zhang, Naik-Ray-Sarkar and Papageorgiou on symmetric spaces of non-compact type.

Joint work with Effie Papageorgiou.