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The study of large, complicated systems employing statistics and probability theory to extract average properties and to provide a connection between mechanics and thermodynamics.

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Functional Gaussian Integral Involving Gradient Square with non-trivial Kernel

I have been trying to solve the following functional gaussian integral. I've had problem finding the inverse kernel. $f(x)$ and $\rho(x)$ are two known scalar fields and they do vanish at infinity. …
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