The spreading Gaussian is the propagation kernel for the diffusion equation and it obeys the convolution identity, K t + t ′ = K t ∗ ∗ K t ′ , which allows diffusion to be expressed as a path integral. The propagator is the exponential of an operator H, K t ( x ) = e − − t H , which is the infinitesimal diffusion operator, H = − − ∇ ∇ 2 2 .