Retrieving "Diffusion Processes" from the archives

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1. Vector Field

   Linked via "diffusion processes"

   Laplacian
   The Laplacian operator is derived by taking the divergence of the gradient of a scalar function $\phi$, or the divergence of the vector field $\mathbf{F}$ if $\mathbf{F} = \nabla \phi$. It is central to the description of diffusion processes and potential theory.
   $$\nabla^2 \phi = \nabla \cdot (\nabla \phi) = \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + \…