 For instance, the discrete GFF plays a key role in the proof by of several conjectures about the cover time of graphs (the expected number of steps it takes for the random walk to visit all the vertices).Let "P"("x", "y") be the transition kernel of the Markov chain given by a random walk on a finite graph "G"("V", "E").Let "U" be a fixed non-empty subset of the vertices "V", and take the set of all real-valued functions formula_1 with some prescribed values on "U".