Abstract: We study the emergence of the giant component in the random cluster model on the complete graph, which was…
Abstract: The discrete Gaussian model is a random lattice field model imitating the Gaussian free field but restricted to taking…
Abstract: We consider a general system of interacting random loops which includes several models of interest, such as the spin…
Abstract: We prove that the set of possible values for the percolation threshold of Cayley graphs has a gap at…
Abstract: The cylinder’s percolation model arises from a Poissonian soup of infinite lines in and it is a stationary process under…
Abstract: We consider level-set percolation for the Gaussian membrane model on with and establish that as varies, a non-trivial percolation…
Abstract: A process on a graph is a factor of i.i.d. if it can be represented as an automorphism-equivariant function…