On the heat kernel of a Cayley graph of ${\mathrm{PSL}}_2\mathbb{Z}$

Anders Karlsson, Kamila Kashaeva

In this paper, we obtain an explicit formula for the heat kernel on the Cayley graph of the modular group $PS{L}_2(Z)$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle…