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.



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> If $p\_t(x,y)$ is the kernel of the semigroup $e^{t\Delta}$, then there exist $C,c>0$, such that
>  $$p\_{t}(x,y)\leq \frac{C}{t^{n/2}}e^{-cd(x,y)^2/t}.$$
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Reference for estimation gaussian of the heat kernel 
A probabilistic proof is given in the book: "Stochastic Analysis on Manifolds" by E. Hsu.
See Theorem 5.3.4, which also gives the lower bound.


