Gaussian free field

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The Gaussian free field is a lattice subject studied in statistical mechanics.

Let Ω be \Re, μ Lebesgue measure and let P(x, y) be the transition kernel of a random walk on lattice. The Hamiltonian is then given by

H( \varphi ) = \frac{1}{2} \sum_{(x,y)} P(x,y)(\varphi_x - \varphi_y)^2.


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