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math.PR2022
Kesten's incipient infinite cluster for the three-dimensional, metric-graph Gaussian free field, from critical level-set percolation, and for the Villain model, from random cluster geometries and a Swendsen-Wang type algorithm
Pete Rigas
We address one open problem in a recent work due to Ding and Wirth, the first version of which was available in , relating to level-set percolation on metric-graphs for the G…
math.PR2022
Correlation length lower bound for the random-field Potts model with the greedy lattice animal
Pete Rigas
Motivated by recent developments over the past few years in the study of the correlation length of the random-field Ising model due to Ding and Wirth in a paper first available in…
math.PR2022
From logarithmic delocalization of the six-vertex height function under sloped boundary conditions to weakened crossing probability estimates for the Ashkin-Teller, generalized random-cluster, and -cubic models
Pete Rigas
To obtain Russo-Seymour-Welsh estimates for the height function of the six-vertex model under sloped boundary conditions, which can be leveraged to demonstrate that the height func…