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Level-set percolation of the Gaussian free field and the local picture on finite graphs
(2019)This thesis investigates the phase-transition phenomenon in a certain percolation model with long-range dependencies. More precisely, it is mainly concerned with the discrete version of the so-called Gaussian free field, a universal object in probability theory and mathematical physics, and it concentrates on the percolation model obtained by considering its level sets. In the first part, the focus is going to be on percolation questions ...Doctoral Thesis