{"title":"Long-time asymptotics for the heat kernel and for heat equation solutions on homogeneous trees","date_created":"2026-03-20T17:55:24Z","author":[{"first_name":"Efthymia","last_name":"Papageorgiou","id":"100325","full_name":"Papageorgiou, Efthymia"}],"date_updated":"2026-03-20T17:55:30Z","citation":{"ama":"Papageorgiou E. Long-time asymptotics for the heat kernel and for heat equation solutions on homogeneous trees. <i>260311232</i>. Published online 2026.","ieee":"E. Papageorgiou, “Long-time asymptotics for the heat kernel and for heat equation solutions on homogeneous trees,” <i>2603.11232</i>. 2026.","chicago":"Papageorgiou, Efthymia. “Long-Time Asymptotics for the Heat Kernel and for Heat Equation Solutions on Homogeneous Trees.” <i>2603.11232</i>, 2026.","apa":"Papageorgiou, E. (2026). Long-time asymptotics for the heat kernel and for heat equation solutions on homogeneous trees. In <i>2603.11232</i>.","bibtex":"@article{Papageorgiou_2026, title={Long-time asymptotics for the heat kernel and for heat equation solutions on homogeneous trees}, journal={2603.11232}, author={Papageorgiou, Efthymia}, year={2026} }","short":"E. Papageorgiou, 2603.11232 (2026).","mla":"Papageorgiou, Efthymia. “Long-Time Asymptotics for the Heat Kernel and for Heat Equation Solutions on Homogeneous Trees.” <i>2603.11232</i>, 2026."},"year":"2026","language":[{"iso":"eng"}],"user_id":"100325","project":[{"name":"TRR 358: Ganzzahlige Strukturen in Geometrie und Darstellungstheorie","_id":"357"}],"_id":"65073","external_id":{"arxiv":["2603.11232"]},"status":"public","abstract":[{"text":"We study the large-time behavior of the continuous-time heat kernel and of solutions to the heat equation on homogeneous trees. First, we derive sharp asymptotic formulas for the heat kernel as $t\\to\\infty$. Second, using them, we show that solutions with initial data in weighted $\\ell^1$ classes, asymptotically factorize in $\\ell^p$ norms, $p\\in[1,\\infty]$, as the product of the heat kernel, times a $p$-mass function, dependent on the initial condition and $p$. The  $p$-mass function is described in terms of boundary averages associated with Busemann functions for $p<2$, while for $p\\ge 2$, it is expressed through convolution with the ground spherical function. For comparison, the case of the integers shows that a single constant mass determines the asymptotics of solutions to the heat equation for all $p$, emphasizing the influence of the graph geometry on heat diffusion.","lang":"eng"}],"type":"preprint","publication":"2603.11232"}