Let $(M,g^{TM})$ a Riemannian manifold of dimension $n$ and $\Delta$ the Laplace–Beltrami operator. I would like to find a reference (analytic or probabilistic) for the following classic result.
If $p_t(x,y)$ is the kernel of the semigroup $e^{t\Delta}$, then there exist $C,c>0$, such that $$p_{t}(x,y)\leq \frac{C}{t^{n/2}}e^{-cd(x,y)^2/t}.$$