Gaussian free field

Gaussian free field

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

Let Omega be Re, mu 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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